A164410 Number of binary strings of length n with no substrings equal to 0000 0001 or 0101

13, 22, 38, 64, 108, 184, 312, 528, 896, 1520, 2576, 4368, 7408, 12560, 21296, 36112, 61232, 103824, 176048, 298512, 506160, 858256, 1455280, 2467600, 4184112, 7094672, 12029872, 20398096, 34587440, 58647184, 99443376, 168618256

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 (1,0,2).

Formula

G.f.: x^4*(13+9*x+16*x^2)/(1-x-2*x^3). - R. J. Mathar, Nov 30 2011

Mathematica

LinearRecurrence[{1, 0, 2}, {13, 22, 38}, 50] (* G. C. Greubel, Sep 19 2017 *)

Prog

(PARI) x='x+O('x^50); Vec(x^4*(13+9*x+16*x^2)/(1-x-2*x^3)) \\ G. C. Greubel, Sep 19 2017

Crossrefs

Sequence in context: A164495 A164427 A164456 * A164421 A164493 A164445

Adjacent sequences: A164407 A164408 A164409 * A164411 A164412 A164413

Keyword

nonn

Author

R. H. Hardin, Aug 14 2009

Status

approved