This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A330892 #43 Dec 19 2024 11:27:31
%S A330892 0,1,0,0,1,0,-3,1,1,0,-8,0,2,1,0,-15,-2,3,3,1,0,-24,-5,4,6,4,1,0,-35,
%T A330892 -9,5,10,9,5,1,0,-48,-14,6,15,16,12,6,1,0,-63,-20,7,21,25,22,15,7,1,0,
%U A330892 -80,-27,8,28,36,35,28,18,8,1,0,-99,-35,9,36,49,51,45,34,21,9,1,0
%N A330892 Square array of polygonal numbers read by descending antidiagonals (the transpose of A317302).
%C A330892 \c 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ...
%C A330892 r\
%C A330892 _0 0 1 0 -3 -8 -15 -24 -35 -48 -63 -80 -99 -120 -143 -168 -195 A067998
%C A330892 _1 0 1 1 0 -2 -5 -9 -14 -20 -27 -35 -44 -54 -65 -77 -90 A080956
%C A330892 _2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 A001477
%C A330892 _3 0 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 A000217
%C A330892 _4 0 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 A000290
%C A330892 _5 0 1 5 12 22 35 51 70 92 117 145 176 210 247 287 330 A000326
%C A330892 _6 0 1 6 15 28 45 66 91 120 153 190 231 276 325 378 435 A000384
%C A330892 _7 0 1 7 18 34 55 81 112 148 189 235 286 342 403 469 540 A000566
%C A330892 _8 0 1 8 21 40 65 96 133 176 225 280 341 408 481 560 645 A000567
%C A330892 _9 0 1 9 24 46 75 111 154 204 261 325 396 474 559 651 750 A001106
%C A330892 10 0 1 10 27 52 85 126 175 232 297 370 451 540 637 742 855 A001107
%C A330892 11 0 1 11 30 58 95 141 196 260 333 415 506 606 715 833 960 A051682
%C A330892 12 0 1 12 33 64 105 156 217 288 369 460 561 672 793 924 1065 A051624
%C A330892 13 0 1 13 36 70 115 171 238 316 405 505 616 738 871 1015 1170 A051865
%C A330892 14 0 1 14 39 76 125 186 259 344 441 550 671 804 949 1106 1275 A051866
%C A330892 15 0 1 15 42 82 135 201 280 372 477 595 726 870 1027 1197 1380 A051867
%C A330892 ...
%C A330892 Each row has a second forward difference of (r-2) and each column has a forward difference of c(c-1)/2.
%H A330892 E. Deza and M. Deza, <a href="http://www.worldscientific.com/doi/suppl/10.1142/8188/suppl_file/8188_chap01.pdf">Figurate Numbers</a>, World Scientific, 2012; see p. 45.
%H A330892 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PolygonalNumber.html">Polygonal Number</a>.
%H A330892 Wikipedia, <a href="https://en.wikipedia.org/wiki/Polygonal_number">Polygonal number</a>.
%H A330892 <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%F A330892 P(r, c) = (r - 2)(c(c-1)/2) + c.
%t A330892 Table[ PolygonalNumber[r - c, c], {r, 0, 11}, {c, r, 0, -1}] // Flatten
%Y A330892 Cf. A317302 (the same array) but read by ascending antidiagonals.
%Y A330892 Sub-arrays: A089000, A139600, A206735;
%Y A330892 Rows: A067998, A080956, A001477, A000217, A000290, A000326, A000384, A000566, A000567, A001106, A001107, A051682, A051624, A051865, A051866, A051867, A051868, A051869, A051870, A051871, A051872, A051873, A051874, A051875, A051876, A255184, A255185, A255186, A161935, A255187, A254474, ..., ;
%Y A330892 Columns (maybe missing some leading terms): A000004, A000012, A001477, A008585, A016957, A017329, A139606, A139607, A139608, A139609, A139610, A139611, A139612, A139613, A139614, A139615, A139616, A139617, A139618, A139619, A139620;
%Y A330892 Diagonals: A256857, A127736, A002411, A006003, A006000, A064808, A060354, A162607, A077414,
%Y A330892 Number of times k>1 appears: A129654, First occurrence of k: A063778.
%K A330892 easy,sign,tabl
%O A330892 1,7
%A A330892 _Robert G. Wilson v_, Apr 27 2020