A203945 - OEIS

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A203945

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

1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0

(list; table; graph; refs; listen; history; text; internal format)

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.

LINKS

Table of n, a(n) for n=1..99.

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]];