Zentrierte Dreieckszahlen

Einleitung

Die zentrierten Dreieckszahlen bezifferndie Anzahl von Kugeln, um ein Dreieck nach folgender Vorschrift zu legen: Es befindet sich eine Kugel im Zentrum und um dieses werden in dreiecksförmigen Schichten weitere Kugeln angeordnet.
Man zählt sie zusammen mit den zentrierten Quadratzahlen , zentrierten Fünfeckszahlen und zentrierten Sechseckszahlen zu den zentrierten Polygonalzahlen.

Formel

Man kann allgemein jede zentrierte Dreieckszahl einer natürliche Zahl n mit folgender Formel berechnen.

Formel für eine zentrierte Dreieckszahl n

Beispiel:
Beispiel einer Berechnung der zentrierten Dreieckszahl von 5

Verzeichnis

 

Zentrierte Dreieckszahl von 0


Hier finden Sie die zentrierte Dreieckszahl von 0.

zd0 = 1

 

Zentrierte Dreieckszahlen von 1 bis 100


Hier finden Sie eine Liste der zentrierten Dreieckszahlen von 1 bis 100.

zd1 → zd10 zd1 = 4zd2 = 10zd3 = 19zd4 = 31zd5 = 46zd6 = 64zd7 = 85zd8 = 109zd9 = 136zd10 = 166
zd11 → zd20 zd11 = 199zd12 = 235zd13 = 274zd14 = 316zd15 = 361zd16 = 409zd17 = 460zd18 = 514zd19 = 571zd20 = 631
zd21 → zd30 zd21 = 694zd22 = 760zd23 = 829zd24 = 901zd25 = 976zd26 = 1054zd27 = 1135zd28 = 1219zd29 = 1306zd30 = 1396
zd31 → zd40 zd31 = 1489zd32 = 1585zd33 = 1684zd34 = 1786zd35 = 1891zd36 = 1999zd37 = 2110zd38 = 2224zd39 = 2341zd40 = 2461
zd41 → zd50 zd41 = 2584zd42 = 2710zd43 = 2839zd44 = 2971zd45 = 3106zd46 = 3244zd47 = 3385zd48 = 3529zd49 = 3676zd50 = 3826
zd51 → zd60 zd51 = 3979zd52 = 4135zd53 = 4294zd54 = 4456zd55 = 4621zd56 = 4789zd57 = 4960zd58 = 5134zd59 = 5311zd60 = 5491
zd61 → zd70 zd61 = 5674zd62 = 5860zd63 = 6049zd64 = 6241zd65 = 6436zd66 = 6634zd67 = 6835zd68 = 7039zd69 = 7246zd70 = 7456
zd71 → zd80 zd71 = 7669zd72 = 7885zd73 = 8104zd74 = 8326zd75 = 8551zd76 = 8779zd77 = 9010zd78 = 9244zd79 = 9481zd80 = 9721
zd81 → zd90 zd81 = 9964zd82 = 10210zd83 = 10459zd84 = 10711zd85 = 10966zd86 = 11224zd87 = 11485zd88 = 11749zd89 = 12016zd90 = 12286
zd91 → zd100 zd91 = 12559zd92 = 12835zd93 = 13114zd94 = 13396zd95 = 13681zd96 = 13969zd97 = 14260zd98 = 14554zd99 = 14851zd100 = 15151

 

Zentrierte Dreieckszahlen von 101 bis 200


Hier finden Sie eine Liste der zentrierten Dreieckszahlen von 101 bis 200.

zd101 → zd110 zd101 = 15454zd102 = 15760zd103 = 16069zd104 = 16381zd105 = 16696zd106 = 17014zd107 = 17335zd108 = 17659zd109 = 17986zd110 = 18316
zd111 → zd120 zd111 = 18649zd112 = 18985zd113 = 19324zd114 = 19666zd115 = 20011zd116 = 20359zd117 = 20710zd118 = 21064zd119 = 21421zd120 = 21781
zd121 → zd130 zd121 = 22144zd122 = 22510zd123 = 22879zd124 = 23251zd125 = 23626zd126 = 24004zd127 = 24385zd128 = 24769zd129 = 25156zd130 = 25546
zd131 → zd140 zd131 = 25939zd132 = 26335zd133 = 26734zd134 = 27136zd135 = 27541zd136 = 27949zd137 = 28360zd138 = 28774zd139 = 29191zd140 = 29611
zd141 → zd150 zd141 = 30034zd142 = 30460zd143 = 30889zd144 = 31321zd145 = 31756zd146 = 32194zd147 = 32635zd148 = 33079zd149 = 33526zd150 = 33976
zd151 → zd160 zd151 = 34429zd152 = 34885zd153 = 35344zd154 = 35806zd155 = 36271zd156 = 36739zd157 = 37210zd158 = 37684zd159 = 38161zd160 = 38641
zd161 → zd170 zd161 = 39124zd162 = 39610zd163 = 40099zd164 = 40591zd165 = 41086zd166 = 41584zd167 = 42085zd168 = 42589zd169 = 43096zd170 = 43606
zd171 → zd180 zd171 = 44119zd172 = 44635zd173 = 45154zd174 = 45676zd175 = 46201zd176 = 46729zd177 = 47260zd178 = 47794zd179 = 48331zd180 = 48871
zd181 → zd190 zd181 = 49414zd182 = 49960zd183 = 50509zd184 = 51061zd185 = 51616zd186 = 52174zd187 = 52735zd188 = 53299zd189 = 53866zd190 = 54436
zd191 → zd200 zd191 = 55009zd192 = 55585zd193 = 56164zd194 = 56746zd195 = 57331zd196 = 57919zd197 = 58510zd198 = 59104zd199 = 59701zd200 = 60301

 

Zentrierte Dreieckszahlen von 201 bis 300


Hier finden Sie eine Liste der zentrierten Dreieckszahlen von 201 bis 300.

zd201 → zd210 zd201 = 60904zd202 = 61510zd203 = 62119zd204 = 62731zd205 = 63346zd206 = 63964zd207 = 64585zd208 = 65209zd209 = 65836zd210 = 66466
zd211 → zd220 zd211 = 67099zd212 = 67735zd213 = 68374zd214 = 69016zd215 = 69661zd216 = 70309zd217 = 70960zd218 = 71614zd219 = 72271zd220 = 72931
zd221 → zd230 zd221 = 73594zd222 = 74260zd223 = 74929zd224 = 75601zd225 = 76276zd226 = 76954zd227 = 77635zd228 = 78319zd229 = 79006zd230 = 79696
zd231 → zd240 zd231 = 80389zd232 = 81085zd233 = 81784zd234 = 82486zd235 = 83191zd236 = 83899zd237 = 84610zd238 = 85324zd239 = 86041zd240 = 86761
zd241 → zd250 zd241 = 87484zd242 = 88210zd243 = 88939zd244 = 89671zd245 = 90406zd246 = 91144zd247 = 91885zd248 = 92629zd249 = 93376zd250 = 94126
zd251 → zd260 zd251 = 94879zd252 = 95635zd253 = 96394zd254 = 97156zd255 = 97921zd256 = 98689zd257 = 99460zd258 = 100234zd259 = 101011zd260 = 101791
zd261 → zd270 zd261 = 102574zd262 = 103360zd263 = 104149zd264 = 104941zd265 = 105736zd266 = 106534zd267 = 107335zd268 = 108139zd269 = 108946zd270 = 109756
zd271 → zd280 zd271 = 110569zd272 = 111385zd273 = 112204zd274 = 113026zd275 = 113851zd276 = 114679zd277 = 115510zd278 = 116344zd279 = 117181zd280 = 118021
zd281 → zd290 zd281 = 118864zd282 = 119710zd283 = 120559zd284 = 121411zd285 = 122266zd286 = 123124zd287 = 123985zd288 = 124849zd289 = 125716zd290 = 126586
zd291 → zd300 zd291 = 127459zd292 = 128335zd293 = 129214zd294 = 130096zd295 = 130981zd296 = 131869zd297 = 132760zd298 = 133654zd299 = 134551zd300 = 135451

 

Zentrierte Dreieckszahlen von 301 bis 400


Hier finden Sie eine Liste der zentrierten Dreieckszahlen von 301 bis 400.

zd301 → zd310 zd301 = 136354zd302 = 137260zd303 = 138169zd304 = 139081zd305 = 139996zd306 = 140914zd307 = 141835zd308 = 142759zd309 = 143686zd310 = 144616
zd311 → zd320 zd311 = 145549zd312 = 146485zd313 = 147424zd314 = 148366zd315 = 149311zd316 = 150259zd317 = 151210zd318 = 152164zd319 = 153121zd320 = 154081
zd321 → zd330 zd321 = 155044zd322 = 156010zd323 = 156979zd324 = 157951zd325 = 158926zd326 = 159904zd327 = 160885zd328 = 161869zd329 = 162856zd330 = 163846
zd331 → zd340 zd331 = 164839zd332 = 165835zd333 = 166834zd334 = 167836zd335 = 168841zd336 = 169849zd337 = 170860zd338 = 171874zd339 = 172891zd340 = 173911
zd341 → zd350 zd341 = 174934zd342 = 175960zd343 = 176989zd344 = 178021zd345 = 179056zd346 = 180094zd347 = 181135zd348 = 182179zd349 = 183226zd350 = 184276
zd351 → zd360 zd351 = 185329zd352 = 186385zd353 = 187444zd354 = 188506zd355 = 189571zd356 = 190639zd357 = 191710zd358 = 192784zd359 = 193861zd360 = 194941
zd361 → zd370 zd361 = 196024zd362 = 197110zd363 = 198199zd364 = 199291zd365 = 200386zd366 = 201484zd367 = 202585zd368 = 203689zd369 = 204796zd370 = 205906
zd371 → zd380 zd371 = 207019zd372 = 208135zd373 = 209254zd374 = 210376zd375 = 211501zd376 = 212629zd377 = 213760zd378 = 214894zd379 = 216031zd380 = 217171
zd381 → zd390 zd381 = 218314zd382 = 219460zd383 = 220609zd384 = 221761zd385 = 222916zd386 = 224074zd387 = 225235zd388 = 226399zd389 = 227566zd390 = 228736
zd391 → zd400 zd391 = 229909zd392 = 231085zd393 = 232264zd394 = 233446zd395 = 234631zd396 = 235819zd397 = 237010zd398 = 238204zd399 = 239401zd400 = 240601

 

Zentrierte Dreieckszahlen von 401 bis 500


Hier finden Sie eine Liste der zentrierten Dreieckszahlen von 401 bis 500.

zd401 → zd410 zd401 = 241804zd402 = 243010zd403 = 244219zd404 = 245431zd405 = 246646zd406 = 247864zd407 = 249085zd408 = 250309zd409 = 251536zd410 = 252766
zd411 → zd420 zd411 = 253999zd412 = 255235zd413 = 256474zd414 = 257716zd415 = 258961zd416 = 260209zd417 = 261460zd418 = 262714zd419 = 263971zd420 = 265231
zd421 → zd430 zd421 = 266494zd422 = 267760zd423 = 269029zd424 = 270301zd425 = 271576zd426 = 272854zd427 = 274135zd428 = 275419zd429 = 276706zd430 = 277996
zd431 → zd440 zd431 = 279289zd432 = 280585zd433 = 281884zd434 = 283186zd435 = 284491zd436 = 285799zd437 = 287110zd438 = 288424zd439 = 289741zd440 = 291061
zd441 → zd450 zd441 = 292384zd442 = 293710zd443 = 295039zd444 = 296371zd445 = 297706zd446 = 299044zd447 = 300385zd448 = 301729zd449 = 303076zd450 = 304426
zd451 → zd460 zd451 = 305779zd452 = 307135zd453 = 308494zd454 = 309856zd455 = 311221zd456 = 312589zd457 = 313960zd458 = 315334zd459 = 316711zd460 = 318091
zd461 → zd470 zd461 = 319474zd462 = 320860zd463 = 322249zd464 = 323641zd465 = 325036zd466 = 326434zd467 = 327835zd468 = 329239zd469 = 330646zd470 = 332056
zd471 → zd480 zd471 = 333469zd472 = 334885zd473 = 336304zd474 = 337726zd475 = 339151zd476 = 340579zd477 = 342010zd478 = 343444zd479 = 344881zd480 = 346321
zd481 → zd490 zd481 = 347764zd482 = 349210zd483 = 350659zd484 = 352111zd485 = 353566zd486 = 355024zd487 = 356485zd488 = 357949zd489 = 359416zd490 = 360886
zd491 → zd500 zd491 = 362359zd492 = 363835zd493 = 365314zd494 = 366796zd495 = 368281zd496 = 369769zd497 = 371260zd498 = 372754zd499 = 374251zd500 = 375751

 

Zentrierte Dreieckszahlen von 501 bis 600


Hier finden Sie eine Liste der zentrierten Dreieckszahlen von 501 bis 600.

zd501 → zd510 zd501 = 377254zd502 = 378760zd503 = 380269zd504 = 381781zd505 = 383296zd506 = 384814zd507 = 386335zd508 = 387859zd509 = 389386zd510 = 390916
zd511 → zd520 zd511 = 392449zd512 = 393985zd513 = 395524zd514 = 397066zd515 = 398611zd516 = 400159zd517 = 401710zd518 = 403264zd519 = 404821zd520 = 406381
zd521 → zd530 zd521 = 407944zd522 = 409510zd523 = 411079zd524 = 412651zd525 = 414226zd526 = 415804zd527 = 417385zd528 = 418969zd529 = 420556zd530 = 422146
zd531 → zd540 zd531 = 423739zd532 = 425335zd533 = 426934zd534 = 428536zd535 = 430141zd536 = 431749zd537 = 433360zd538 = 434974zd539 = 436591zd540 = 438211
zd541 → zd550 zd541 = 439834zd542 = 441460zd543 = 443089zd544 = 444721zd545 = 446356zd546 = 447994zd547 = 449635zd548 = 451279zd549 = 452926zd550 = 454576
zd551 → zd560 zd551 = 456229zd552 = 457885zd553 = 459544zd554 = 461206zd555 = 462871zd556 = 464539zd557 = 466210zd558 = 467884zd559 = 469561zd560 = 471241
zd561 → zd570 zd561 = 472924zd562 = 474610zd563 = 476299zd564 = 477991zd565 = 479686zd566 = 481384zd567 = 483085zd568 = 484789zd569 = 486496zd570 = 488206
zd571 → zd580 zd571 = 489919zd572 = 491635zd573 = 493354zd574 = 495076zd575 = 496801zd576 = 498529zd577 = 500260zd578 = 501994zd579 = 503731zd580 = 505471
zd581 → zd590 zd581 = 507214zd582 = 508960zd583 = 510709zd584 = 512461zd585 = 514216zd586 = 515974zd587 = 517735zd588 = 519499zd589 = 521266zd590 = 523036
zd591 → zd600 zd591 = 524809zd592 = 526585zd593 = 528364zd594 = 530146zd595 = 531931zd596 = 533719zd597 = 535510zd598 = 537304zd599 = 539101zd600 = 540901

 

Zentrierte Dreieckszahlen von 601 bis 700


Hier finden Sie eine Liste der zentrierten Dreieckszahlen von 601 bis 700.

zd601 → zd610 zd601 = 542704zd602 = 544510zd603 = 546319zd604 = 548131zd605 = 549946zd606 = 551764zd607 = 553585zd608 = 555409zd609 = 557236zd610 = 559066
zd611 → zd620 zd611 = 560899zd612 = 562735zd613 = 564574zd614 = 566416zd615 = 568261zd616 = 570109zd617 = 571960zd618 = 573814zd619 = 575671zd620 = 577531
zd621 → zd630 zd621 = 579394zd622 = 581260zd623 = 583129zd624 = 585001zd625 = 586876zd626 = 588754zd627 = 590635zd628 = 592519zd629 = 594406zd630 = 596296
zd631 → zd640 zd631 = 598189zd632 = 600085zd633 = 601984zd634 = 603886zd635 = 605791zd636 = 607699zd637 = 609610zd638 = 611524zd639 = 613441zd640 = 615361
zd641 → zd650 zd641 = 617284zd642 = 619210zd643 = 621139zd644 = 623071zd645 = 625006zd646 = 626944zd647 = 628885zd648 = 630829zd649 = 632776zd650 = 634726
zd651 → zd660 zd651 = 636679zd652 = 638635zd653 = 640594zd654 = 642556zd655 = 644521zd656 = 646489zd657 = 648460zd658 = 650434zd659 = 652411zd660 = 654391
zd661 → zd670 zd661 = 656374zd662 = 658360zd663 = 660349zd664 = 662341zd665 = 664336zd666 = 666334zd667 = 668335zd668 = 670339zd669 = 672346zd670 = 674356
zd671 → zd680 zd671 = 676369zd672 = 678385zd673 = 680404zd674 = 682426zd675 = 684451zd676 = 686479zd677 = 688510zd678 = 690544zd679 = 692581zd680 = 694621
zd681 → zd690 zd681 = 696664zd682 = 698710zd683 = 700759zd684 = 702811zd685 = 704866zd686 = 706924zd687 = 708985zd688 = 711049zd689 = 713116zd690 = 715186
zd691 → zd700 zd691 = 717259zd692 = 719335zd693 = 721414zd694 = 723496zd695 = 725581zd696 = 727669zd697 = 729760zd698 = 731854zd699 = 733951zd700 = 736051

 

Zentrierte Dreieckszahlen von 701 bis 800


Hier finden Sie eine Liste der zentrierten Dreieckszahlen von 701 bis 800.

zd701 → zd710 zd701 = 738154zd702 = 740260zd703 = 742369zd704 = 744481zd705 = 746596zd706 = 748714zd707 = 750835zd708 = 752959zd709 = 755086zd710 = 757216
zd711 → zd720 zd711 = 759349zd712 = 761485zd713 = 763624zd714 = 765766zd715 = 767911zd716 = 770059zd717 = 772210zd718 = 774364zd719 = 776521zd720 = 778681
zd721 → zd730 zd721 = 780844zd722 = 783010zd723 = 785179zd724 = 787351zd725 = 789526zd726 = 791704zd727 = 793885zd728 = 796069zd729 = 798256zd730 = 800446
zd731 → zd740 zd731 = 802639zd732 = 804835zd733 = 807034zd734 = 809236zd735 = 811441zd736 = 813649zd737 = 815860zd738 = 818074zd739 = 820291zd740 = 822511
zd741 → zd750 zd741 = 824734zd742 = 826960zd743 = 829189zd744 = 831421zd745 = 833656zd746 = 835894zd747 = 838135zd748 = 840379zd749 = 842626zd750 = 844876
zd751 → zd760 zd751 = 847129zd752 = 849385zd753 = 851644zd754 = 853906zd755 = 856171zd756 = 858439zd757 = 860710zd758 = 862984zd759 = 865261zd760 = 867541
zd761 → zd770 zd761 = 869824zd762 = 872110zd763 = 874399zd764 = 876691zd765 = 878986zd766 = 881284zd767 = 883585zd768 = 885889zd769 = 888196zd770 = 890506
zd771 → zd780 zd771 = 892819zd772 = 895135zd773 = 897454zd774 = 899776zd775 = 902101zd776 = 904429zd777 = 906760zd778 = 909094zd779 = 911431zd780 = 913771
zd781 → zd790 zd781 = 916114zd782 = 918460zd783 = 920809zd784 = 923161zd785 = 925516zd786 = 927874zd787 = 930235zd788 = 932599zd789 = 934966zd790 = 937336
zd791 → zd800 zd791 = 939709zd792 = 942085zd793 = 944464zd794 = 946846zd795 = 949231zd796 = 951619zd797 = 954010zd798 = 956404zd799 = 958801zd800 = 961201

 

Zentrierte Dreieckszahlen von 801 bis 900


Hier finden Sie eine Liste der zentrierten Dreieckszahlen von 801 bis 900.

zd801 → zd810 zd801 = 963604zd802 = 966010zd803 = 968419zd804 = 970831zd805 = 973246zd806 = 975664zd807 = 978085zd808 = 980509zd809 = 982936zd810 = 985366
zd811 → zd820 zd811 = 987799zd812 = 990235zd813 = 992674zd814 = 995116zd815 = 997561zd816 = 1000009zd817 = 1002460zd818 = 1004914zd819 = 1007371zd820 = 1009831
zd821 → zd830 zd821 = 1012294zd822 = 1014760zd823 = 1017229zd824 = 1019701zd825 = 1022176zd826 = 1024654zd827 = 1027135zd828 = 1029619zd829 = 1032106zd830 = 1034596
zd831 → zd840 zd831 = 1037089zd832 = 1039585zd833 = 1042084zd834 = 1044586zd835 = 1047091zd836 = 1049599zd837 = 1052110zd838 = 1054624zd839 = 1057141zd840 = 1059661
zd841 → zd850 zd841 = 1062184zd842 = 1064710zd843 = 1067239zd844 = 1069771zd845 = 1072306zd846 = 1074844zd847 = 1077385zd848 = 1079929zd849 = 1082476zd850 = 1085026
zd851 → zd860 zd851 = 1087579zd852 = 1090135zd853 = 1092694zd854 = 1095256zd855 = 1097821zd856 = 1100389zd857 = 1102960zd858 = 1105534zd859 = 1108111zd860 = 1110691
zd861 → zd870 zd861 = 1113274zd862 = 1115860zd863 = 1118449zd864 = 1121041zd865 = 1123636zd866 = 1126234zd867 = 1128835zd868 = 1131439zd869 = 1134046zd870 = 1136656
zd871 → zd880 zd871 = 1139269zd872 = 1141885zd873 = 1144504zd874 = 1147126zd875 = 1149751zd876 = 1152379zd877 = 1155010zd878 = 1157644zd879 = 1160281zd880 = 1162921
zd881 → zd890 zd881 = 1165564zd882 = 1168210zd883 = 1170859zd884 = 1173511zd885 = 1176166zd886 = 1178824zd887 = 1181485zd888 = 1184149zd889 = 1186816zd890 = 1189486
zd891 → zd900 zd891 = 1192159zd892 = 1194835zd893 = 1197514zd894 = 1200196zd895 = 1202881zd896 = 1205569zd897 = 1208260zd898 = 1210954zd899 = 1213651zd900 = 1216351

 

Zentrierte Dreieckszahlen von 901 bis 1000


Hier finden Sie eine Liste der zentrierten Dreieckszahlen von 901 bis 1000.

zd901 → zd910 zd901 = 1219054zd902 = 1221760zd903 = 1224469zd904 = 1227181zd905 = 1229896zd906 = 1232614zd907 = 1235335zd908 = 1238059zd909 = 1240786zd910 = 1243516
zd911 → zd920 zd911 = 1246249zd912 = 1248985zd913 = 1251724zd914 = 1254466zd915 = 1257211zd916 = 1259959zd917 = 1262710zd918 = 1265464zd919 = 1268221zd920 = 1270981
zd921 → zd930 zd921 = 1273744zd922 = 1276510zd923 = 1279279zd924 = 1282051zd925 = 1284826zd926 = 1287604zd927 = 1290385zd928 = 1293169zd929 = 1295956zd930 = 1298746
zd931 → zd940 zd931 = 1301539zd932 = 1304335zd933 = 1307134zd934 = 1309936zd935 = 1312741zd936 = 1315549zd937 = 1318360zd938 = 1321174zd939 = 1323991zd940 = 1326811
zd941 → zd950 zd941 = 1329634zd942 = 1332460zd943 = 1335289zd944 = 1338121zd945 = 1340956zd946 = 1343794zd947 = 1346635zd948 = 1349479zd949 = 1352326zd950 = 1355176
zd951 → zd960 zd951 = 1358029zd952 = 1360885zd953 = 1363744zd954 = 1366606zd955 = 1369471zd956 = 1372339zd957 = 1375210zd958 = 1378084zd959 = 1380961zd960 = 1383841
zd961 → zd970 zd961 = 1386724zd962 = 1389610zd963 = 1392499zd964 = 1395391zd965 = 1398286zd966 = 1401184zd967 = 1404085zd968 = 1406989zd969 = 1409896zd970 = 1412806
zd971 → zd980 zd971 = 1415719zd972 = 1418635zd973 = 1421554zd974 = 1424476zd975 = 1427401zd976 = 1430329zd977 = 1433260zd978 = 1436194zd979 = 1439131zd980 = 1442071
zd981 → zd990 zd981 = 1445014zd982 = 1447960zd983 = 1450909zd984 = 1453861zd985 = 1456816zd986 = 1459774zd987 = 1462735zd988 = 1465699zd989 = 1468666zd990 = 1471636
zd991 → zd1000 zd991 = 1474609zd992 = 1477585zd993 = 1480564zd994 = 1483546zd995 = 1486531zd996 = 1489519zd997 = 1492510zd998 = 1495504zd999 = 1498501zd1000 = 1501501