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

0,6

Comments

Column 1 of A118884.

Links

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

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

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

Example

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

Maple

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

Crossrefs

Cf. A118884.

Sequence in context: A107035 A260145 A260778 * A097392 A373046 A090634

Adjacent sequences: A118882 A118883 A118884 * A118886 A118887 A118888

Keyword

nonn

Author

Emeric Deutsch, May 03 2006

Status

approved