A164396 Number of binary strings of length n with no substrings equal to 0001 or 0110.

1, 2, 4, 8, 14, 24, 41, 70, 120, 205, 350, 597, 1018, 1736, 2960, 5047, 8605, 14671, 25013, 42645, 72706, 123957, 211335, 360306, 614287, 1047300, 1785545, 3044181, 5190033, 8848502, 15085836, 25719884, 43849902, 74759820, 127458225, 217303882

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

Formula

a(n) = 2*a(n-1) - a(n-3) + a(n-5) - a(n-6). - Andrew Howroyd, Feb 14 2018

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

Mathematica

LinearRecurrence[{2, 0, -1, 0, 1, -1}, {1, 2, 4, 8, 14, 24}, 50] (* G. C. Greubel, Sep 18 2017 *)

Prog

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

Crossrefs

Sequence in context: A178982 A164397 A164174 * A164400 A164405 A164163

Adjacent sequences: A164393 A164394 A164395 * A164397 A164398 A164399

Keyword

nonn

Author

R. H. Hardin, Aug 14 2009

Extensions

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

Status

approved