A164401 Number of binary strings of length n with no substrings equal to 0010 or 0101.

1, 2, 4, 8, 14, 25, 45, 81, 146, 264, 477, 861, 1554, 2805, 5063, 9139, 16497, 29779, 53754, 97031, 175150, 316162, 570702, 1030171, 1859556, 3356674, 6059113, 10937270, 19742803, 35637620, 64329263, 116120383, 209608236, 378362622, 682980194, 1232843622

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,-1,1,0,0,1).

Formula

a(n) = 2*a(n-1) - a(n-2) + a(n-3) + a(n-6). - Andrew Howroyd, Feb 14 2018

G.f.: (1 + x^2 + x^3 + x^5)/(1 - 2*x + x^2 - x^3 - x^6). - R. J. Mathar, Nov 30 2011

Mathematica

LinearRecurrence[{2, -1, 1, 0, 0, 1}, {1, 2, 4, 8, 14, 25}, 50] (* G. C. Greubel, Sep 18 2017 *)

Prog

(PARI) Vec((1 + x^2 + x^3 + x^5)/(1 - 2*x + x^2 - x^3 - x^6) + O(x^40)) \\ G. C. Greubel, Sep 18 2017

Crossrefs

Sequence in context: A199925 A164388 A164389 * A164387 A164150 A164149

Adjacent sequences: A164398 A164399 A164400 * A164402 A164403 A164404

Keyword

nonn

Author

R. H. Hardin, Aug 14 2009

Extensions

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

Status

approved