A118892 Number of binary sequences of length n containing exactly one subsequence 0110.

0, 0, 0, 0, 1, 4, 12, 30, 70, 156, 339, 722, 1515, 3140, 6444, 13116, 26513, 53280, 106530, 212062, 420503, 830964, 1637055, 3216240, 6303099, 12324816, 24049953, 46841550, 91074760, 176796340, 342696000, 663363750, 1282457260, 2476394580

Offset

0,6

Comments

Column 1 of A118890. Convolution of A059633 with itself (disregard the 0 terms).

Links

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (4,-4,-2,6,-4,-1,2,-1)

Formula

G.f.=z^4/(1-2z+z^3-z^4)^2.

+(-n+4)*a(n) +2*(n-3)*a(n-1) +(-n+1)*a(n-3) +n*a(n-4)=0. - R. J. Mathar, Jul 26 2022

Example

a(5)=4 because we have 01100,01101,00110 and 10110.

Maple

G:=z^4/(1-2*z+z^3-z^4)^2: Gser:=series(G, z=0, 37): seq(coeff(Gser, z, n), n=0..34);

Crossrefs

Cf. A118890, A049864, A059633.

Sequence in context: A272144 A036389 A037166 * A036388 A100691 A000298

Adjacent sequences: A118889 A118890 A118891 * A118893 A118894 A118895

Keyword

nonn

Author

Emeric Deutsch, May 04 2006

Status

approved