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 A117906 #6 Oct 21 2021 01:30:42
%S A117906 1,-1,1,0,0,1,0,-1,0,1,0,0,0,-1,1,0,0,-1,0,0,1,0,0,0,0,-1,0,1,0,0,0,0,
%T A117906 0,0,-1,1,0,0,0,0,0,-1,0,0,1,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,0,0,0,0,
%U A117906 -1,1,0,0,0,0,0,0,0,0,-1,0,0,1,0,0,0,0,0,0,0,0,0,0,-1,0,1
%N A117906 Inverse of number triangle A117904.
%C A117906 Row sums are (1, 0, 1, 0, 0, 0, ...) with g.f. 1 + x^2.
%C A117906 Diagonal sums are A117907.
%H A117906 G. C. Greubel, <a href="/A117906/b117906.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A117906 G.f.: (1 -x*(1-y) +x^2*y^2 -x^3*y -x^5*y^2)/(1-x^3*y^3).
%e A117906 Triangle begins
%e A117906 1;
%e A117906 -1, 1;
%e A117906 0, 0, 1;
%e A117906 0, -1, 0, 1;
%e A117906 0, 0, 0, -1, 1;
%e A117906 0, 0, -1, 0, 0, 1;
%e A117906 0, 0, 0, 0, -1, 0, 1;
%e A117906 0, 0, 0, 0, 0, 0, -1, 1;
%e A117906 0, 0, 0, 0, 0, -1, 0, 0, 1;
%e A117906 0, 0, 0, 0, 0, 0, 0, -1, 0, 1;
%e A117906 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1;
%e A117906 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1;
%e A117906 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1;
%e A117906 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1;
%e A117906 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1;
%t A117906 M[n_, k_]:= M[n, k]= If[k>n, 0, If[Abs[JacobiSymbol[Binomial[n, 2], 3] - JacobiSymbol[Binomial[k, 2], 3]]==0, 1, 0]];
%t A117906 m:= m= With[{q=20}, Table[M[n, k], {n,0,q}, {k,0,q}]];
%t A117906 T[n_, k_]:= Inverse[m][[n+1, k+1]];
%t A117906 Table[T[n, k], {n,0,15}, {k,0,n}]//Flatten (* _G. C. Greubel_, Oct 20 2021 *)
%Y A117906 Cf. A117904, A117907.
%K A117906 easy,sign,tabl
%O A117906 0,1
%A A117906 _Paul Barry_, Apr 01 2006