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A164394 Number of binary strings of length n with no substrings equal to 0001 or 0100. 1
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 (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)

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

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Last modified November 19 19:37 EST 2018. Contains 317364 sequences. (Running on oeis4.)