A164429 Number of binary strings of length n with no substrings equal to 0000, 0011, or 1011.

1, 2, 4, 8, 13, 21, 33, 50, 75, 112, 166, 245, 361, 531, 780, 1145, 1680, 2464, 3613, 5297, 7765, 11382, 16683, 24452, 35838, 52525, 76981, 112823, 165352, 242337, 355164, 520520, 762861, 1118029, 1638553, 2401418, 3519451, 5158008, 7559430, 11078885, 16236897

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,-1,1,-1).

Formula

G.f.: (x+1)*(x^2+1)*(x^2-x+1)/((x-1)*(x^3+x-1)). - R. J. Mathar, Jan 19 2011

a(n) = a(n-1) + a(n-3) + 4 for n>4. - Greg Dresden, Feb 09 2020

Mathematica

LinearRecurrence[{2, -1, 1, -1}, {1, 2, 4, 8, 13, 21}, 41] (* Harvey P. Dale, Sep 02 2017; amended for offset 0 by Georg Fischer, Apr 02 2019 *)

Prog

(PARI) x='x+O('x^50); Vec((x+1)*(x^2+1)*(x^2-x+1)/((x-1)*(x^3+x-1))) \\ Georg Fischer, Apr 02 2019

Crossrefs

Sequence in context: A218913 A349061 A241691 * A073336 A164420 A164457

Adjacent sequences: A164426 A164427 A164428 * A164430 A164431 A164432

Keyword

nonn,easy

Author

R. H. Hardin, Aug 14 2009

Extensions

Edited by Alois P. Heinz, Oct 11 2017

Status

approved