A164389 Number of binary strings of length n with no substrings equal to 0000 or 0101.

1, 2, 4, 8, 14, 25, 45, 81, 145, 260, 467, 838, 1503, 2697, 4840, 8684, 15581, 27958, 50166, 90012, 161509, 289799, 519989, 933019, 1674126, 3003903, 5389930, 9671201, 17353133, 31136896, 55869228, 100246695, 179873620, 322748972, 579111590, 1039105525

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 (1,0,2,1)

Formula

G.f.: -(x+1)*(x^2+1)^2/(x^4+2*x^3+x-1). - R. J. Mathar, Dec 01 2011

Mathematica

LinearRecurrence[{1, 0, 2, 1}, {1, 2, 4, 8, 14, 25}, 50] (* G. C. Greubel, Sep 18 2017; amended for offset 0 by Georg Fischer, Apr 02 2019 *)

Prog

(PARI) x='x+O('x^50); Vec(((x+1)*(x^2+1)^2)/(1-x-2*x^3-x^4)) \\ G. C. Greubel, Sep 18 2017; amended for offset 0 by Georg Fischer, Apr 02 2019

Crossrefs

Sequence in context: A281810 A199925 A164388 * A164401 A164387 A164150

Adjacent sequences: A164386 A164387 A164388 * A164390 A164391 A164392

Keyword

nonn,easy

Author

R. H. Hardin, Aug 14 2009

Extensions

Edited by Alois P. Heinz, Oct 11 2017

Status

approved