A118885 Number of binary sequences of length n containing exactly one subsequence 0011.

0, 0, 0, 0, 1, 4, 12, 32, 78, 180, 400, 864, 1827, 3800, 7800, 15840, 31884, 63704, 126480, 249760, 490885, 960828, 1873828, 3642560, 7060314, 13649196, 26324704, 50662464, 97309767, 186571248, 357119472, 682524224, 1302589016, 2482706544

Offset: 0

Author

Emeric Deutsch, May 03 2006

Keywords

• nonn

Comments

Column 1 of A118884.

Examples

			a(5)=4 because we have 00110,00111,00011 and 10011.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-4,0,-2,4,0,0,-1).

Crossrefs

Cf. A118884.

Programs

Maple

g:=z^4/(1-2*z+z^4)^2: gser:=series(g,z=0,40): seq(coeff(gser,z,n),n=0..36);

Formula

G.f. x^4 / ( (x-1)^2*(x^3+x^2+x-1)^2 ).

a(n) -2*a(n-1) + a(n-2) = A073778(n). - R. J. Mathar, Jul 26 2022