A164402 Number of binary strings of length n with no substrings equal to 0010 or 0110.

1, 2, 4, 8, 14, 24, 40, 68, 116, 200, 344, 592, 1016, 1744, 2992, 5136, 8816, 15136, 25984, 44608, 76576, 131456, 225664, 387392, 665024, 1141632, 1959808, 3364352, 5775488, 9914624, 17020160, 29218048, 50157824, 86104576, 147813376, 253747200

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,-2,2)

Formula

a(n) = 2*a(n-1) - 2*a(n-3) + 2*a(n-4). - Andrew Howroyd, Feb 14 2018

G.f.: (1 + 2*x^3)/(1 - 2*x + 2*x^3 - 2*x^4). - R. J. Mathar, Nov 30 2011

Mathematica

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

Prog

(PARI) Vec((1 + 2*x^3)/(1 - 2*x + 2*x^3 - 2*x^4) + O(x^40)) \\ G. C. Greubel, Sep 19 2017

Crossrefs

Sequence in context: A019274 A164173 A164162 * A164165 A164168 A182747

Adjacent sequences: A164399 A164400 A164401 * A164403 A164404 A164405

Keyword

nonn

Author

R. H. Hardin, Aug 14 2009

Extensions

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

Status

approved