

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
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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^2x+1)/((x1)*(x^3+x1)).  R. J. Mathar, Jan 19 2011
a(n) = a(n1) + a(n3) + 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^2x+1)/((x1)*(x^3+x1))) \\ 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



