cp's OEIS Frontend

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.

A118407 Triangle, read by rows, equal to the matrix square of triangle A118404; also equals the matrix inverse of triangle A118401.

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%I A118407 #3 Mar 30 2012 18:36:57
%S A118407 1,0,1,-2,0,1,2,-2,0,1,0,2,-2,0,1,-2,0,2,-2,0,1,4,-2,0,2,-2,0,1,-6,4,
%T A118407 -2,0,2,-2,0,1,4,-6,4,-2,0,2,-2,0,1,6,4,-6,4,-2,0,2,-2,0,1,-20,6,4,-6,
%U A118407 4,-2,0,2,-2,0,1,26,-20,6,4,-6,4,-2,0,2,-2,0,1,-12,26,-20,6,4,-6,4,-2,0,2,-2,0,1
%N A118407 Triangle, read by rows, equal to the matrix square of triangle A118404; also equals the matrix inverse of triangle A118401.
%C A118407 This triangle has an integer matrix square-root (A118404) if the main diagonal of the square-root is allowed to be signed. Even though the columns of this triangle are all the same, the columns of the matrix square-root A118404 are all different.
%F A118407 G.f.: A(x,y) = (1+x)^2/(1+x^2)/(1+2*x+2*x^2)/(1-x*y). Column g.f.: (1+x)^2/(1+x^2)/(1+2*x+2*x^2).
%e A118407 Triangle begins:
%e A118407 1;
%e A118407 0, 1;
%e A118407 -2, 0, 1;
%e A118407 2,-2, 0, 1;
%e A118407 0, 2,-2, 0, 1;
%e A118407 -2, 0, 2,-2, 0, 1;
%e A118407 4,-2, 0, 2,-2, 0, 1;
%e A118407 -6, 4,-2, 0, 2,-2, 0, 1;
%e A118407 4,-6, 4,-2, 0, 2,-2, 0, 1;
%e A118407 6, 4,-6, 4,-2, 0, 2,-2, 0, 1;
%e A118407 -20, 6, 4,-6, 4,-2, 0, 2,-2, 0, 1;
%e A118407 26,-20, 6, 4,-6, 4,-2, 0, 2,-2, 0, 1; ...
%o A118407 (PARI) {T(n,k)=polcoeff(polcoeff((1+x)^2/(1+x^2)/(1+2*x+2*x^2)/(1-x*y+x*O(x^n)),n,x)+y*O(y^k),k,y)}
%Y A118407 Cf. A118404 (matrix square-root), A118401 (matrix inverse), A118408 (row sums), A118409 (unsigned row sums).
%K A118407 sign,tabl
%O A118407 0,4
%A A118407 _Paul D. Hanna_, Apr 27 2006