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A164429 Number of binary strings of length n with no substrings equal to 0000, 0011, or 1011. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A259964 A218913 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

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Last modified August 3 13:59 EDT 2021. Contains 346438 sequences. (Running on oeis4.)