

A203953


Symmetric matrix based on (1,2,1,2,1,2,...), by antidiagonals.


3



1, 2, 2, 1, 5, 1, 2, 4, 4, 2, 1, 5, 6, 5, 1, 2, 4, 6, 6, 4, 2, 1, 5, 6, 10, 6, 5, 1, 2, 4, 6, 8, 8, 6, 4, 2, 1, 5, 6, 10, 11, 10, 6, 5, 1, 2, 4, 6, 8, 10, 10, 8, 6, 4, 2, 1, 5, 6, 10, 11, 15, 11, 10, 6, 5, 1, 2, 4, 6, 8, 10, 12, 12, 10, 8, 6, 4, 2, 1, 5, 6, 10, 11, 15, 16, 15, 11, 10
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OFFSET

1,2


COMMENTS

Let s be the periodic sequence (1,2,1,2,1,2,...) 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 A203951 represents the matrix product M=T'*T. M is the selffusion matrix of s, as defined at A193722. See A203954 for characteristic polynomials of principal submatrices of M, with interlacing zeros.


LINKS



EXAMPLE

Northwest corner:
1 2 1 2 1 2 1
2 5 4 5 4 5 4
1 3 6 6 6 6 6


MATHEMATICA

t = {1, 2}; 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] (* A203953 *)
m[i_, j_] := M[[i]][[j]];
Flatten[Table[m[i, n + 1  i], {n, 1, 12}, {i, 1, n}]]


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



