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A164401 Number of binary strings of length n with no substrings equal to 0010 or 0101. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 7 05:22 EST 2022. Contains 358649 sequences. (Running on oeis4.)