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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
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.
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
Sequence in context: A322549 A349645 A237996 * A323591 A105348 A016406
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Jan 08 2012
STATUS
approved