A164405 Number of binary strings of length n with no substrings equal to 0010 or 1100.

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

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