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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 (list; graph; refs; listen; history; text; internal format)
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(n-1) - a(n-3) + a(n-6). - 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(n-1)-a(n-3)+a(n-6), seq(a(i)=[14, 24, 41, 70, 120, 207][i-3], 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

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Last modified December 9 06:07 EST 2021. Contains 349627 sequences. (Running on oeis4.)