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A203947 Symmetric matrix based on (1,0,1,1,0,1,1,0,1,...), by antidiagonals.

%I A203947 #6 Jul 12 2012 00:39:54
%S A203947 1,0,0,1,1,1,1,0,0,1,0,1,2,1,0,1,1,1,1,1,1,1,0,1,3,1,0,1,0,1,2,1,1,2,
%T A203947 1,0,1,1,1,2,3,2,1,1,1,1,0,1,3,1,1,3,1,0,1,0,1,2,1,2,4,2,1,2,1,0,1,1,
%U A203947 1,2,3,2,2,3,2,1,1,1,1,0,1,3,1,2,5,2,1,3,1,0,1,0,1,2,1,2,4,2,2
%N A203947 Symmetric matrix based on (1,0,1,1,0,1,1,0,1,...), by antidiagonals.
%C A203947 Let s be the periodic sequence (1,0,1,1,0,1,...)  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 A203947 represents the matrix product M=T'*T.  M is the self-fusion matrix of s, as defined at A193722.  See A203948 for characteristic polynomials of principal submatrices of M, with interlacing zeros.
%e A203947 Northwest corner:
%e A203947 1 0 1 1 0 1 1 0
%e A203947 0 1 0 1 1 0 1 1
%e A203947 1 0 2 1 1 0 1 1
%e A203947 1 1 1 3 1 2 3 1
%e A203947 0 1 1 1 3 1 2 3
%e A203947 1 0 2 2 1 4 2 2
%e A203947 1 1 1 3 2 2 5 2
%t A203947 t = {1, 0, 1};
%t A203947 t1 = Flatten[{t, t, t, t, t, t, t, t, t, t}];
%t A203947 s[k_] := t1[[k]];
%t A203947 U = NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[
%t A203947    Table[s[k], {k, 1, 15}]];
%t A203947 L = Transpose[U]; M = L.U; TableForm[M]  (* A203947 *)
%t A203947 m[i_, j_] := M[[i]][[j]];
%t A203947 Flatten[Table[m[i, n + 1 - i], {n, 1, 12}, {i, 1, n}]]
%Y A203947 Cf. A203948, A202453.
%K A203947 nonn,tabl
%O A203947 1,13
%A A203947 _Clark Kimberling_, Jan 08 2012