A143282 Number of binary words of length n containing at least one subword 1001 and no subwords 10^{i}1 with i<2.

0, 0, 0, 0, 1, 2, 3, 5, 9, 15, 24, 38, 60, 94, 146, 225, 345, 527, 802, 1216, 1838, 2771, 4168, 6256, 9372, 14016, 20929, 31208, 46476, 69133, 102726, 152494, 226171, 335169, 496320, 734440, 1086102, 1605187, 2371049, 3500522, 5165573, 7619251

Offset: 0

Author

Alois P. Heinz, Aug 04 2008

Keywords

• nonn

Examples

			a(7) = 5 because 5 binary words of length 7 have at least one subword 1001 and no subwords 11 or 101: 0001001, 0010010, 0100100, 1001000, 1001001.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000930, A003269, 2nd column of A143291.

Programs

Maple

a:= n-> (Matrix (7, (i, j)-> `if` (i=j-1, 1, `if` (i=7, [-1, 0, -1, 0, 1, -1, 2][j], 0)))^n. <<(0$6), 1>>)[3, 1]: seq (a(n), n=0..50);

Mathematica

CoefficientList[Series[x^4/((x^3+x-1)*(x^4+x-1)), {x,0,50}], x] (* G. C. Greubel, Apr 29 2017 *)

PARI

x='x+O('x^50); concat([0,0,0,0], Vec(x^4/((x^3+x-1)*(x^4+x-1)))) \\ G. C. Greubel, Apr 29 2017

Formula

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

a(n) = A000930(n+2) - A003269(n+4).