A164399 Number of binary strings of length n with no substrings equal to 0001 or 1010

14, 24, 41, 70, 119, 202, 343, 582, 987, 1674, 2839, 4814, 8163, 13842, 23471, 39798, 67483, 114426, 194023, 328990, 557843, 945890, 1603871, 2719558, 4611339, 7819082, 13258199, 22480878, 38119043, 64635442, 109597199, 185835286

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,-1,2,-2).

Formula

G.f.: x^4*(-14+4*x-7*x^2+16*x^3)/((1-x)*(2*x^3+x-1)). - R. J. Mathar, Nov 30 2011

Mathematica

LinearRecurrence[{2, -1, 2, -2}, {14, 24, 41, 70}, 50] (* G. C. Greubel, Sep 18 2017 *)

Prog

(PARI) x='x+O('x^50); Vec(x^4*(-14+4*x-7*x^2+16*x^3)/((1-x)*(2*x^3+x-1))) \\ G. C. Greubel, Sep 18 2017

Crossrefs

Sequence in context: A171124 A046290 A111743 * A164404 A211323 A141838

Adjacent sequences: A164396 A164397 A164398 * A164400 A164401 A164402

Keyword

nonn

Author

R. H. Hardin, Aug 14 2009

Status

approved