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 A117945 #13 Feb 21 2024 08:18:58
%S A117945 1,0,1,-1,0,1,0,0,0,1,0,0,0,0,1,0,0,0,-1,0,1,-1,0,0,0,0,0,1,0,-1,0,0,
%T A117945 0,0,0,1,1,0,-1,0,0,0,-1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
%U A117945 1,0,0,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1
%N A117945 Triangle related to powers of 3 partitions of n.
%C A117945 Row sums are A039966.
%C A117945 Inverse of A117944.
%H A117945 G. C. Greubel, <a href="/A117945/b117945.txt">Rows n = 0..50 of the triangle, flattened</a>
%e A117945 Triangle begins
%e A117945 1;
%e A117945 0, 1;
%e A117945 -1, 0, 1;
%e A117945 0, 0, 0, 1;
%e A117945 0, 0, 0, 0, 1;
%e A117945 0, 0, 0, -1, 0, 1;
%e A117945 -1, 0, 0, 0, 0, 0, 1;
%e A117945 0, -1, 0, 0, 0, 0, 0, 1;
%e A117945 1, 0, -1, 0, 0, 0, -1, 0, 1;
%e A117945 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e A117945 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e A117945 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1;
%t A117945 M[n_, k_]:= M[n, k] = If[k>n, 0, Mod[Sum[JacobiSymbol[Binomial[n, j], 3]*JacobiSymbol[Binomial[n-j, k], 3], {j,0,n}], 2], 0];
%t A117945 m:= m= With[{q=60}, Table[M[n, k], {n,0,q}, {k,0,q}]];
%t A117945 T[n_, k_]:= Inverse[m][[n+1, k+1]];
%t A117945 Table[T[n, k], {n,0,15}, {k,0,n}]//Flatten (* _G. C. Greubel_, Oct 29 2021 *)
%Y A117945 Cf. A039966, A117944.
%K A117945 sign,tabl
%O A117945 0,1
%A A117945 _Paul Barry_, Apr 05 2006