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

Author

Emeric Deutsch, May 04 2006

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A118890, A049864, A059633.

Programs

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);

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