A203949 Symmetric matrix based on (1,1,0,1,1,0,1,1,0,...), by antidiagonals.

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

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: A262257 A144474 A298602 * A070200 A359833 A025914

Adjacent sequences: A203946 A203947 A203948 * A203950 A203951 A203952

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 08 2012

Status

approved