

A164405


Number of binary strings of length n with no substrings equal to 0010 or 1100.


1



1, 2, 4, 8, 14, 24, 41, 70, 120, 207, 358, 620, 1074, 1860, 3220, 5573, 9644, 16688, 28877, 49970, 86472, 149640, 258954, 448124, 775485, 1341986, 2322320, 4018795, 6954558, 12034920, 20826530, 36040488, 62368376, 107929017, 186772104, 323210752
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OFFSET

0,2


LINKS

R. H. Hardin, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (2,0,1,0,0,1).


FORMULA

a(n) = 2*a(n1)  a(n3) + a(n6).  Andrew Howroyd, Feb 14 2018
G.f.: (1 + x^3)/(1  2*x + x^3  x^6).  R. J. Mathar, Nov 30 2011


MAPLE

f:= gfun:rectoproc({a(n) = 2*a(n1)a(n3)+a(n6), seq(a(i)=[14, 24, 41, 70, 120, 207][i3], i=4..9)}, a(n), remember):
map(f, [$0..35]); # Robert Israel, Sep 19 2017


MATHEMATICA

LinearRecurrence[{2, 0, 1, 0, 0, 1}, {1, 2, 4, 8, 14, 24}, 50] (* G. C. Greubel, Sep 19 2017 *)


PROG

(PARI) Vec((1 + x^3)/(1  2*x + x^3  x^6) + O(x^40)) \\ G. C. Greubel, Sep 19 2017


CROSSREFS

Sequence in context: A164174 A164396 A164400 * A164163 A164395 A164160
Adjacent sequences: A164402 A164403 A164404 * A164406 A164407 A164408


KEYWORD

nonn


AUTHOR

R. H. Hardin, Aug 14 2009


EXTENSIONS

a(0)a(3) prepended by Andrew Howroyd, Feb 14 2018


STATUS

approved



