A164406 Number of binary strings of length n with no substrings equal to 0011 or 0101.

1, 2, 4, 8, 14, 24, 41, 68, 111, 180, 289, 460, 728, 1146, 1795, 2800, 4352, 6742, 10414, 16044, 24659, 37818, 57885, 88440, 134899, 205448, 312448, 474548, 719861, 1090734, 1650908, 2496260, 3770910, 5691360, 8582653, 12932512, 19472363, 29298540, 44053525

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

Formula

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

a(n) = Sum_{i=0..floor((n+1)/2)} (n+1-2i) * C(n+1-2i,i). - Wesley Ivan Hurt, Nov 17 2017

Mathematica

LinearRecurrence[{2, -1, 2, -2, 0, -1}, {14, 24, 41, 68, 111, 180}, 50] (* G. C. Greubel, Sep 19 2017 *)

Prog

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

Crossrefs

Sequence in context: A164165 A164168 A182747 * A178982 A164397 A164174

Adjacent sequences: A164403 A164404 A164405 * A164407 A164408 A164409

Keyword

nonn,easy

Author

R. H. Hardin, Aug 14 2009

Extensions

Edited by Alois P. Heinz, Oct 27 2017

Status

approved