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 A194801 #55 Aug 24 2024 09:45:32 %S A194801 0,0,1,0,1,0,0,1,1,3,0,1,2,4,1,0,1,3,5,4,6,0,1,4,6,7,9,3,0,1,5,7,10, %T A194801 12,9,10,0,1,6,8,13,15,15,16,6,0,1,7,9,16,18,21,22,16,15,0,1,8,10,19, %U A194801 21,27,28,26,25,10,0,1,9,11,22,24,33,34,36,35 %N A194801 Square array read by antidiagonals: T(n,k) = k*((n+1)*k-n+1)/2, k = 0, +- 1, +- 2,..., n >= 0. %C A194801 Note that a single formula gives several types of numbers. Row 0 lists 0 together the Molien series for 3-dimensional group [2,k]+ = 22k. Row 1 lists, except first zero, the squares repeated. If n >= 2, row n lists the generalized (n+3)-gonal numbers, for example: row 2 lists the generalized pentagonal numbers A001318. See some other examples in the cross-references section. %e A194801 Array begins: %e A194801 (A008795): 0, 1, 0, 3, 1, 6, 3, 10, 6, 15, 10... %e A194801 (A008794): 0, 1, 1, 4, 4, 9, 9, 16, 16, 25, 25... %e A194801 A001318: 0, 1, 2, 5, 7, 12, 15, 22, 26, 35, 40... %e A194801 A000217: 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55... %e A194801 A085787: 0, 1, 4, 7, 13, 18, 27, 34, 46, 55, 70... %e A194801 A001082: 0, 1, 5, 8, 16, 21, 33, 40, 56, 65, 85... %e A194801 A118277: 0, 1, 6, 9, 19, 24, 39, 46, 66, 75, 100... %e A194801 A074377: 0, 1, 7, 10, 22, 27, 45, 52, 76, 85, 115... %e A194801 A195160: 0, 1, 8, 11, 25, 30, 51, 58, 86, 95, 130... %e A194801 A195162: 0, 1, 9, 12, 28, 33, 57, 64, 96, 105, 145... %e A194801 A195313: 0, 1, 10, 13, 31, 36, 63, 70, 106, 115, 160... %e A194801 A195818: 0, 1, 11, 14, 34, 39, 69, 76, 116, 125, 175... %o A194801 (GW-BASIC) %o A194801 100 'SQUARE ARRAY T(N,K) A194801 %o A194801 200 DIM T(11,10) %o A194801 210 FOR N=0 TO 11 %o A194801 220 FOR J=0 TO 5 %o A194801 230 IF J>0 THEN T(N,K)= J *((N+1)* J -N+1)/2: K=K+1 %o A194801 240 T(N,K)=(-J)*((N+1)*(-J)-N+1)/2: K=K+1 %o A194801 250 NEXT J %o A194801 260 K=0 %o A194801 270 NEXT N %o A194801 299 '... %o A194801 300 'PRINT SQUARE ARRAY T(N,K) (see example) %o A194801 310 FOR N=0 TO 11 %o A194801 320 FOR K=0 TO 10 %o A194801 330 PRINT T(N,K); %o A194801 340 NEXT K %o A194801 350 PRINT %o A194801 360 NEXT N %o A194801 500 END %Y A194801 Rows (0-11): 0 together with A008795, (truncated A008794), A001318, A000217, A085787, A001082, A118277, A074377, A195160, A195162, A195313, A195818 %Y A194801 Columns (0-9): A000004, A000012, A001477, (truncated A000027), A016777, (truncated A008585), A016945, (truncated A016957), A017341, (truncated A017329). %Y A194801 Cf. A139600. %K A194801 nonn,tabl %O A194801 0,10 %A A194801 _Omar E. Pol_, Feb 05 2012