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A203951 Symmetric matrix based on (1,0,0,0,1,0,0,0,...), by antidiagonals. 4
1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,41

COMMENTS

Let s be the periodic sequence (1,0,0,0,1,0,0,0,...) 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 A203951 represents the matrix product M=T'*T.  M is the self-fusion matrix of s, as defined at A193722.  See A203952 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 0 1 0 0 0 1 0

0 1 0 0 0 1 0 0 0 1

0 0 1 0 0 0 1 0 0 0

0 0 0 1 0 0 0 1 0 0

1 0 0 0 2 0 0 0 2 0

0 1 0 0 0 2 0 0 0 2

0 0 1 0 0 0 2 0 0 0

0 0 0 1 0 0 0 2 0 0

1 0 0 0 2 0 0 0 3 0

MATHEMATICA

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

f[k_] := t1[[k]];

U[n_] :=

  NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[

   Table[f[k], {k, 1, n}]];

L[n_] := Transpose[U[n]];

p[n_] := CharacteristicPolynomial[L[n].U[n], x];

c[n_] := CoefficientList[p[n], x]

TableForm[Flatten[Table[p[n], {n, 1, 10}]]]

Table[c[n], {n, 1, 12}]

Flatten[%]  (* A203952 *)

CROSSREFS

Cf. A203951, A202453.

Sequence in context: A111594 A322549 A237996 * A323591 A105348 A016406

Adjacent sequences:  A203948 A203949 A203950 * A203952 A203953 A203954

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 08 2012

STATUS

approved

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Last modified February 16 04:47 EST 2019. Contains 320140 sequences. (Running on oeis4.)