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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
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.
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
Sequence in context: A016408 A316868 A106822 * A309142 A064532 A321922
KEYWORD
tabl,sign
AUTHOR
Clark Kimberling, Jan 08 2012
STATUS
approved