A130902 a(n) is the number of binary strings of length n such that there exist 4 or more ones in a subsequence of length 5 or less.

0, 0, 0, 1, 6, 16, 39, 91, 207, 463, 1014, 2188, 4671, 9888, 20786, 43435, 90302, 186934, 385547, 792642, 1625035, 3323393, 6782041, 13813588, 28087444, 57023945, 115614136, 234117510, 473564782, 956961354, 1932059363, 3897575310, 7856867785, 15827584881

Offset: 0

Author

Tanya Khovanova, Sep 28 2007

Keywords

• nonn

Links

• Matthew House, Table of n, a(n) for n = 0..3304
• Index entries for linear recurrences with constant coefficients, signature (3,-1,-2,1,0,-4,-1,2,0,-1,2).

Crossrefs

Cf. A118647, A118646.

Programs

Mathematica

LinearRecurrence[{3,-1,-2,1,0,-4,-1,2,0,-1,2},{0,0,0,1,6,16,39,91,207,463,1014},40] (* Harvey P. Dale, Jul 19 2020 *)

Formula

a(n) = 2^n - A125513(n).

G.f.: x^3*(-1-3*x+x^2+x^3-x^4+x^5+x^6) / ( (2*x-1)*(x^10+x^7-2*x^5-x^4-x^2-x+1) ). - R. J. Mathar, Nov 28 2011

Extensions

More terms from Matthew House, Dec 26 2016