

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
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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 nth row is formed by putting n1 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 selffusion 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



