

A203949


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


4



1, 1, 1, 0, 2, 0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 0, 2, 1, 1, 2, 0, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 0, 2, 1, 1, 4, 1, 1, 2, 0, 1, 1, 1, 3, 2, 2, 3, 1, 1, 1, 1, 1, 2, 2, 2, 4, 2, 2, 2, 1, 1, 0, 2, 1, 1, 4, 2, 2, 4, 1, 1, 2, 0, 1, 1, 1, 3, 2, 2, 5, 2, 2, 3, 1, 1, 1, 1, 1, 2, 2, 2, 4, 3, 3
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OFFSET

1,5


COMMENTS

Let s be the periodic sequence (1,1,0,1,1,0,...) 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 A203949 represents the matrix product M=T'*T. M is the selffusion matrix of s, as defined at A193722. See A203950 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 1 0 1 1 0 1 1 0 1
1 2 1 1 2 1 1 2 1 1
0 1 2 1 1 2 1 1 2 1
1 1 1 3 2 1 3 2 1 3
1 2 1 2 4 2 2 4 2 2
0 1 2 1 2 4 2 2 4 2
1 1 1 3 2 2 5 3 2 5


MATHEMATICA

t = {1, 1, 0}; t1 = Flatten[{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] (* A203949 *)
m[i_, j_] := M[[i]][[j]];
Flatten[Table[m[i, n + 1  i], {n, 1, 12}, {i, 1, n}]]


CROSSREFS

Cf. A203950, A202453.
Sequence in context: A194341 A171905 A144474 * A070200 A025914 A025916
Adjacent sequences: A203946 A203947 A203948 * A203950 A203951 A203952


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Jan 08 2012


STATUS

approved



