A164391 Number of binary strings of length n with no substrings equal to 0000 or 0111.

1, 2, 4, 8, 14, 25, 44, 77, 134, 233, 405, 703, 1220, 2117, 3673, 6372, 11054, 19176, 33265, 57705, 100101, 173645, 301221, 522526, 906422, 1572363, 2727565, 4731484, 8207665, 14237766, 24698130, 42843633, 74320480, 128923094, 223641776, 387949454, 672972561

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..2000 (first 500 terms from R. H. Hardin)

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

Formula

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

a(n) = 1.6443631... * 1.7346913...^n + O(1), where 1.7346913... is the real root of x^5 - x^3 - 2x^2 - 2x - 1. [Charles R Greathouse IV, Jan 18 2012]

Mathematica

LinearRecurrence[{1, 1, 1, 0, -1, -1}, {14, 25, 44, 77, 134, 233}, 50] (* G. C. Greubel, Sep 18 2017 *)

Prog

(PARI) x='x+O('x^50); Vec(x^4*(-14-11*x-5*x^2+6*x^3+12*x^4+8*x^5)/((1-x)*(x^5+2*x^4+2*x^3+ x^2-1))) \\ G. C. Greubel, Sep 18 2017

Crossrefs

Sequence in context: A210145 A020956 A164393 * A164153 A212588 A164392

Adjacent sequences: A164388 A164389 A164390 * A164392 A164393 A164394

Keyword

nonn,easy

Author

R. H. Hardin, Aug 14 2009

Extensions

Conjectured g.f. verified by Charles R Greathouse IV, Jan 18 2012

Edited by Alois P. Heinz, Oct 12 2017

Status

approved