OFFSET

1,25

COMMENTS

Let s be the periodic sequence (1,0,0,1,0,0,...) 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 A203945 represents the matrix product M=T'*T. M is the self-fusion matrix of s, as defined at A193722. See A203946 for characteristic polynomials of principal submatrices of M, with interlacing zeros.

EXAMPLE

Northwest corner:

1...0...0...1...0...0...1

0...1...0...0...1...0...0

0...0...1...0...0...1...0

1...0...0...2...0...0...2

0...1...0...0...2...0...0

MATHEMATICA

t = {1, 0, 0}; t1 = Flatten[{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]

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