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

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

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: A242192 A016380 A341354 * A212663 A341774 A015692

Adjacent sequences: A203942 A203943 A203944 * A203946 A203947 A203948

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 08 2012

Status

approved