A164394 Number of binary strings of length n with no substrings equal to 0001 or 0100.

1, 2, 4, 8, 14, 24, 42, 74, 130, 228, 400, 702, 1232, 2162, 3794, 6658, 11684, 20504, 35982, 63144, 110810, 194458, 341250, 598852, 1050912, 1844222, 3236384, 5679458, 9966754, 17490434, 30693572, 53863464, 94523790, 165877688, 291095050, 510836202

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)

Formula

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

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

a(n) = 2*A005251(n + 2) for n > 0. - Andrew Howroyd, Feb 14 2018

Maple

a:= n-> (<<0|1|0>, <0|0|1>, <1|-1|2>>^n. <<2, 2, 4>>)[1, 1]-0^n:
seq(a(n), n=0..40);  # Alois P. Heinz, Feb 14 2018

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A164163 A164395 A164160 * A164171 A164159 A164172

Adjacent sequences: A164391 A164392 A164393 * A164395 A164396 A164397

Keyword

nonn

Author

R. H. Hardin, Aug 14 2009

Extensions

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

Status

approved