A209231 - OEIS

A209231

Number of binary words of length n such that there is at least one 0 and every run of consecutive 0's is of length >= 4.

0, 0, 0, 0, 1, 3, 6, 10, 15, 22, 33, 51, 80, 125, 193, 295, 449, 684, 1045, 1600, 2451, 3752, 5738, 8770, 13403, 20488, 31326, 47903, 73251, 112003, 171244, 261812, 400284, 612008, 935736, 1430709, 2187495, 3344566, 5113646, 7818463, 11953990

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OFFSET

0,6

LINKS

Table of n, a(n) for n=0..40.

FORMULA

O.g.f.: x^4/((1-x)*(1-2*x+x^2-x^5)), see Mathematica code for unsimplified form.

EXAMPLE

a(5) = 3 because we have: {0,0,0,0,0}, {0,0,0,0,1}, {1,0,0,0,0}.

MATHEMATICA

nn=40; a=x^4/(1-x); CoefficientList[Series[(a+1)/((1-a x/(1-x)))*1/(1-x)-1/(1-x), {x, 0, nn}], x]

CROSSREFS

Cf. A000225, A077855, A130578.

Sequence in context: A265071 A330910 A226239 * A137358 A143963 A139714

Adjacent sequences: A209228 A209229 A209230 * A209232 A209233 A209234

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Jan 12 2013

STATUS

approved