cp's OEIS Frontend

A203949 Symmetric matrix based on (1,1,0,1,1,0,1,1,0,...), by antidiagonals.

%I A203949 #6 Jul 12 2012 00:39:54
%S A203949 1,1,1,0,2,0,1,1,1,1,1,1,2,1,1,0,2,1,1,2,0,1,1,1,3,1,1,1,1,1,2,2,2,2,
%T A203949 1,1,0,2,1,1,4,1,1,2,0,1,1,1,3,2,2,3,1,1,1,1,1,2,2,2,4,2,2,2,1,1,0,2,
%U A203949 1,1,4,2,2,4,1,1,2,0,1,1,1,3,2,2,5,2,2,3,1,1,1,1,1,2,2,2,4,3,3
%N A203949 Symmetric matrix based on (1,1,0,1,1,0,1,1,0,...), by antidiagonals.
%C A203949 Let s be the periodic sequence (1,1,0,1,1,0,...)  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 A203949 represents the matrix product M=T'*T.  M is the self-fusion matrix of s, as defined at A193722.  See A203950 for characteristic polynomials of principal submatrices of M, with interlacing zeros.
%e A203949 Northwest corner:
%e A203949 1 1 0 1 1 0 1 1 0 1
%e A203949 1 2 1 1 2 1 1 2 1 1
%e A203949 0 1 2 1 1 2 1 1 2 1
%e A203949 1 1 1 3 2 1 3 2 1 3
%e A203949 1 2 1 2 4 2 2 4 2 2
%e A203949 0 1 2 1 2 4 2 2 4 2
%e A203949 1 1 1 3 2 2 5 3 2 5
%t A203949 t = {1, 1, 0}; t1 = Flatten[{t, t, t, t, t, t, t, t, t}];
%t A203949 s[k_] := t1[[k]];
%t A203949 U = NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[
%t A203949    Table[s[k], {k, 1, 15}]];
%t A203949 L = Transpose[U]; M = L.U; TableForm[M] (* A203949 *)
%t A203949 m[i_, j_] := M[[i]][[j]];
%t A203949 Flatten[Table[m[i, n + 1 - i], {n, 1, 12}, {i, 1, n}]]
%Y A203949 Cf. A203950, A202453.
%K A203949 nonn,tabl
%O A203949 1,5
%A A203949 _Clark Kimberling_, Jan 08 2012