OFFSET
1,13
COMMENTS
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.
EXAMPLE
Northwest corner:
1 0 1 1 0 1 1 0
0 1 0 1 1 0 1 1
1 0 2 1 1 0 1 1
1 1 1 3 1 2 3 1
0 1 1 1 3 1 2 3
1 0 2 2 1 4 2 2
1 1 1 3 2 2 5 2
MATHEMATICA
t = {1, 0, 1};
t1 = Flatten[{t, t, t, t, t, t, t, t, t, t}];
s[k_] := t1[[k]];
U = NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[
Table[s[k], {k, 1, 15}]];
L = Transpose[U]; M = L.U; TableForm[M] (* A203947 *)
m[i_, j_] := M[[i]][[j]];
Flatten[Table[m[i, n + 1 - i], {n, 1, 12}, {i, 1, n}]]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Jan 08 2012
STATUS
approved