

A203905


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


3



1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 2, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 3, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 3, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 3, 3, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET

1,13


COMMENTS

Let s be the periodic sequence (1,0,1,0,1,0,...) and let T be the infinite square matrix whose nth row is formed by putting n1 zeros before the terms of s. Let T' be the transpose of T. Then A203905 represents the matrix product M=T'*T. M is the selffusion matrix of s, as defined at A193722. See A203906 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...1...0...1...0...1...0
0...1...0...1...0...1...0...1
1...0...2...0...2...0...2...0
0...1...0...2...0...2...0...2
1...0...2...0...3...0...3...0


MATHEMATICA

t = {1, 0}; 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] (* A203905 *)
m[i_, j_] := M[[i]][[j]];
Flatten[Table[m[i, n + 1  i], {n, 1, 12}, {i, 1, n}]]


CROSSREFS

Cf. A203906, A202453.
Sequence in context: A016408 A316868 A106822 * A309142 A064532 A321922
Adjacent sequences: A203902 A203903 A203904 * A203906 A203907 A203908


KEYWORD

tabl,sign


AUTHOR

Clark Kimberling, Jan 08 2012


STATUS

approved



