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 A118923 #19 Dec 13 2021 17:29:30
%S A118923 1,1,0,1,1,0,1,2,1,1,1,3,3,2,0,1,4,6,5,2,0,1,5,10,11,7,2,1,1,6,15,21,
%T A118923 18,9,3,0,1,7,21,36,39,27,12,3,0,1,8,28,57,75,66,39,15,3,1,1,9,36,85,
%U A118923 132,141,105,54,18,4,0,1,10,45,121,217,273,246,159,72,22,4,0,1,11,55,166
%N A118923 Triangle T(n,k) built by placing T(n,0)=A000012(n) in the left edge, T(n,n)=A079978(n) on the right edge and filling the body with the Pascal recurrence T(n,k) = T(n-1,k) + T(n-1,k-1).
%C A118923 The fourth diagonal is 1, 2, 5, 11, 21, ..., which is 1 + A000292. The fifth diagonal is 0, 2, 7, 18, 39, 75, 132, 217, 338, 504, 725, 1012, ..., which is A051743.
%C A118923 The array A007318 is generated by placing A000012 on both edges with the same Pascal-like recurrence, and the array A059259 uses edges defined by A000012 and A059841. - _R. J. Mathar_, Jan 21 2008
%C A118923 From _Michael A. Allen_, Nov 30 2021: (Start)
%C A118923 T(n,n-k) is the (n,k)-th entry of the (1/(1-x^3), x/(1-x)) Riordan array.
%C A118923 Sums of rows give A077947.
%C A118923 Sums of antidiagonals give A079962. (End)
%F A118923 From _Michael A. Allen_, Nov 30 2021: (Start)
%F A118923 For 0 <= k < n, T(n,k) = (n-k)*Sum_{j=0..floor(k/3)} binomial(n-3*j,n-k)/(n-3*j).
%F A118923 G.f.: 1/((1+x*y+(x*y)^2)*(1-x-x*y)). (End)
%e A118923 The table begins
%e A118923 1
%e A118923 1 0
%e A118923 1 1 0
%e A118923 1 2 1 1
%e A118923 1 3 3 2 0
%e A118923 1 4 6 5 2 0
%e A118923 1 5 10 11 7 2 1
%e A118923 1 6 15 21 18 9 3 0
%p A118923 A000012 := proc(n) 1 ; end: A079978 := proc(n) if n mod 3 = 0 then 1; else 0 ; fi ; end: A118923 := proc(n,k) if k = 0 then A000012(n); elif k = n then A079978(n) ; else A118923(n-1,k)+A118923(n-1,k-1) ; fi ; end: for n from 0 to 15 do for k from 0 to n do printf("%d, ",A118923(n,k)) ; od: od: # _R. J. Mathar_, Jan 21 2008
%t A118923 Flatten@Table[CoefficientList[Series[1/((1 + x*y + x^2*y^2)(1 - x - x*y)), {x, 0, 23}, {y, 0, 11}], {x, y}][[n + 1, k + 1]], {n, 0, 11}, {k, 0, n}] (* _Michael A. Allen_, Nov 30 2021 *)
%Y A118923 Cf. A000292, A079978, A008620, A079998, A051743, A077947.
%Y A118923 Generalization of A007318, A059259.
%K A118923 easy,nonn,tabl
%O A118923 0,8
%A A118923 _Alford Arnold_, May 05 2006
%E A118923 Edited and extended by _R. J. Mathar_, Jan 21 2008
%E A118923 Offset changed by _Michael A. Allen_, Nov 30 2021