

A164406


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


2



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


FORMULA

G.f.: (x^2+1)/(x^3+x1)^2.  R. J. Mathar, Nov 30 2011
a(n) = Sum_{i=0..floor((n+1)/2)} (n+12i) * C(n+12i,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+x1)^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



