A143287 Number of binary words of length n containing at least one subword 10^{7}1 and no subwords 10^{i}1 with i<7.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 14, 20, 28, 38, 50, 64, 80, 99, 123, 155, 198, 255, 329, 423, 540, 684, 861, 1080, 1354, 1700, 2139, 2696, 3400, 4285, 5392, 6772, 8490, 10630, 13300, 16637, 20812, 26036, 32568, 40726, 50902, 63582, 79372

Offset: 0

Author

Alois P. Heinz, Aug 04 2008

Keywords

• nonn
• easy

Examples

			a(10)=2 because 2 binary words of length 10 have at least one subword 10^{7}1 and no subwords 10^{i}1 with i<7: 0100000001, 1000000010.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2, -1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, -1).

Crossrefs

Cf. A005710, A005711, 7th column of A143291.

Programs

Magma

[n le 9 select 0 else n le 17 select n-9 else 2*Self(n-1)-Self(n-2) +Self(n-8)-Self(n-10)-Self(n-17): n in [1..60]]; // Vincenzo Librandi, Jun 05 2013

Maple

a:= n-> coeff(series(x^9/((x^8+x-1)*(x^9+x-1)), x, n+1), x, n):
seq(a(n), n=0..60);

Mathematica

CoefficientList[Series[x^9 / ((x^8 + x - 1) (x^9 + x - 1)), {x, 0, 60}], x] (* Vincenzo Librandi, Jun 04 2013 *)

Formula

G.f.: x^9/((x^8+x-1)*(x^9+x-1)).

a(n) = A005710(n+7)-A005711(n+7).

a(n) = 2*a(n-1) - a(n-2) + a(n-8) - a(n-10) - a(n-17). - Vincenzo Librandi, Jun 05 2013