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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 (list; table; graph; refs; listen; history; text; internal format)
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 n-th row is formed by putting n-1 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 self-fusion 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

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Last modified November 25 18:32 EST 2014. Contains 250000 sequences.