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 A203905 #6 Jul 12 2012 00:39:54
%S A203905 1,0,0,1,1,1,0,0,0,0,1,1,2,1,1,0,0,0,0,0,0,1,1,2,2,2,1,1,0,0,0,0,0,0,
%T A203905 0,0,1,1,2,2,3,2,2,1,1,0,0,0,0,0,0,0,0,0,0,1,1,2,2,3,3,3,2,2,1,1,0,0,
%U A203905 0,0,0,0,0,0,0,0,0,0,1,1,2,2,3,3,4,3,3,2,2,1,1,0,0,0,0,0,0,0,0
%N A203905 Symmetric matrix based on (1,0,1,0,1,0,1,0,...), by antidiagonals.
%C A203905 Let s be the periodic sequence (1,0,1,0,1,0,...) and let T be the infinite square matrix whose n-th row is formed by putting n-1 zeros before the terms of s. Let T' be the transpose of T. Then A203905 represents the matrix product M=T'*T. M is the self-fusion matrix of s, as defined at A193722. See A203906 for characteristic polynomials of principal submatrices of M, with interlacing zeros.
%e A203905 Northwest corner:
%e A203905 1...0...1...0...1...0...1...0
%e A203905 0...1...0...1...0...1...0...1
%e A203905 1...0...2...0...2...0...2...0
%e A203905 0...1...0...2...0...2...0...2
%e A203905 1...0...2...0...3...0...3...0
%t A203905 t = {1, 0}; t1 = Flatten[{t, t, t, t, t, t, t, t, t, t}];
%t A203905 s[k_] := t1[[k]];
%t A203905 U = NestList[Most[Prepend[#, 0]] &, #,
%t A203905 Length[#] - 1] &[Table[s[k], {k, 1, 15}]];
%t A203905 L = Transpose[U]; M = L.U; TableForm[M] (* A203905 *)
%t A203905 m[i_, j_] := M[[i]][[j]];
%t A203905 Flatten[Table[m[i, n + 1 - i], {n, 1, 12}, {i, 1, n}]]
%Y A203905 Cf. A203906, A202453.
%K A203905 tabl,sign
%O A203905 1,13
%A A203905 _Clark Kimberling_, Jan 08 2012