A164400 Number of binary strings of length n with no substrings equal to 0001 or 1100.

1, 2, 4, 8, 14, 24, 41, 70, 120, 206, 354, 609, 1048, 1804, 3106, 5348, 9209, 15858, 27308, 47026, 80982, 139457, 240156, 413568, 712198, 1226464, 2112073, 3637166, 6263504, 10786278, 18574874, 31987489, 55085136, 94861220, 163358970, 281317836, 484452889

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 (2,0,0,-2,1).

Formula

G.f.: (x^6+x^5-1)/((x-1)*(x^4-x^3-x^2-x+1)). - R. J. Mathar, Nov 28 2011

Mathematica

LinearRecurrence[{2, 0, 0, -2, 1}, {1, 2, 4, 8, 14, 24, 41}, 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((1-x^5-x^6)/((1-x)*(x^4-x^3-x^2-x+1))) \\ G. C. Greubel, Sep 18 2017; amended for offset 0 by Georg Fischer, Apr 02 2019

Crossrefs

Sequence in context: A164397 A164174 A164396 * A164405 A164163 A164395

Adjacent sequences: A164397 A164398 A164399 * A164401 A164402 A164403

Keyword

nonn,easy

Author

R. H. Hardin, Aug 14 2009

Extensions

Edited by Alois P. Heinz, Oct 11 2017

Status

approved