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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 (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,-1,2,-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

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Last modified December 2 12:01 EST 2021. Contains 349440 sequences. (Running on oeis4.)