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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 (list; table; graph; refs; listen; history; text; internal format)
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 n-th row is formed by putting n-1 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 self-fusion 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

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Last modified October 26 06:08 EDT 2021. Contains 348257 sequences. (Running on oeis4.)