A203947 Symmetric matrix based on (1,0,1,1,0,1,1,0,1,...), by antidiagonals.

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

Offset

1,13

Comments

Let s be the periodic sequence (1,0,1,1,0,1,...) 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 A203947 represents the matrix product M=T'*T. M is the self-fusion matrix of s, as defined at A193722. See A203948 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 0 1 1 0 1 1 0
0 1 0 1 1 0 1 1
1 0 2 1 1 0 1 1
1 1 1 3 1 2 3 1
0 1 1 1 3 1 2 3
1 0 2 2 1 4 2 2
1 1 1 3 2 2 5 2

Mathematica

t = {1, 0, 1};
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]  (* A203947 *)
m[i_, j_] := M[[i]][[j]];
Flatten[Table[m[i, n + 1 - i], {n, 1, 12}, {i, 1, n}]]

Crossrefs

Cf. A203948, A202453.

Sequence in context: A191907 A052343 A073484 * A081396 A194293 A349595

Adjacent sequences: A203944 A203945 A203946 * A203948 A203949 A203950

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 08 2012

Status

approved