A164395 Number of binary strings of length n with no substrings equal to 0001 or 0101.

1, 2, 4, 8, 14, 24, 42, 72, 122, 208, 354, 600, 1018, 1728, 2930, 4968, 8426, 14288, 24226, 41080, 69658, 118112, 200274, 339592, 575818, 976368, 1655554, 2807192, 4759930, 8071040, 13685426, 23205288, 39347370, 66718224, 113128802, 191823544

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,-1,2,-2).

Formula

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

G.f.: (1 + x^2)/((1 - x)*(1 - x - 2*x^3)). - R. J. Mathar, Dec 01 2011

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A164400 A164405 A164163 * A164160 A164394 A164171

Adjacent sequences: A164392 A164393 A164394 * A164396 A164397 A164398

Keyword

nonn

Author

R. H. Hardin, Aug 14 2009

Extensions

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

Status

approved