A164456 Number of binary strings of length n with no substrings equal to 0001 0011 or 1000.

13, 22, 37, 63, 108, 185, 318, 547, 941, 1620, 2789, 4802, 8269, 14239, 24520, 42225, 72714, 125219, 215637, 371344, 639485, 1101246, 1896437, 3265823, 5624020, 9685033, 16678438, 28721667, 49461117, 85176188, 146680533, 252596170

Offset

4,1

Links

R. H. Hardin, Table of n, a(n) for n=4..500

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

Formula

G.f.: -x^4*(13-4*x-7*x^2-11*x^3+8*x^4) / ( (x-1)*(x^4-x^3-x^2-x+1) ). - R. J. Mathar, Jan 19 2011

Mathematica

LinearRecurrence[{2, 0, 0, -2, 1}, {13, 22, 37, 63, 108}, 40] (* Harvey P. Dale, Dec 03 2022 *)

Crossrefs

Sequence in context: A164501 A164495 A164427 * A164410 A164421 A164493

Adjacent sequences: A164453 A164454 A164455 * A164457 A164458 A164459

Keyword

nonn,easy

Author

R. H. Hardin, Aug 14 2009

Status

approved