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A203945 Symmetric matrix based on (1,0,0,1,0,0,1,0,0,...), by antidiagonals. 3
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]];

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

Cf. A203946, A202453.

Sequence in context: A057918 A242192 A016380 * A212663 A015692 A016232

Adjacent sequences:  A203942 A203943 A203944 * A203946 A203947 A203948

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 08 2012

STATUS

approved

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Last modified November 13 16:08 EST 2019. Contains 329106 sequences. (Running on oeis4.)