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A265725 Number of binary strings of length n having at least one run of length at least 4. 0
0, 0, 0, 0, 2, 6, 16, 40, 94, 214, 476, 1040, 2242, 4782, 10112, 21232, 44318, 92046, 190364, 392264, 805746, 1650518, 3372816, 6877656, 13998142, 28442918, 57707324, 116925600, 236630274, 478372062, 966145664, 1949583456, 3930972094, 7920443038, 15948482236 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

A "run" is a contiguous block of consecutive identical terms.

LINKS

Table of n, a(n) for n=0..34.

FORMULA

a(n) = 2^n - 2*A000073(n+2).

a(n) = 2*A050231(n-1) for n>0.

G.f.: 2*x^4/((2*x-1)*(x^3+x^2+x-1)). - Alois P. Heinz, Dec 14 2015

EXAMPLE

For n=5 there are 6 such strings: 00000, 00001, 01111, and their complements.

PROG

(PARI) x='x+O('x^100); concat(vector(4), Vec(2*x^4/((2*x-1)*(x^3+x^2+x-1)))) \\ Altug Alkan, Dec 14 2015

CROSSREFS

Cf. A000073, A050231, A167821.

Sequence in context: A198951 A078774 A174016 * A129952 A057711 A302239

Adjacent sequences:  A265722 A265723 A265724 * A265726 A265727 A265728

KEYWORD

nonn

AUTHOR

Jeffrey Shallit, Dec 14 2015

EXTENSIONS

More terms from Alois P. Heinz, Dec 14 2015

STATUS

approved

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Last modified June 18 18:52 EDT 2019. Contains 324215 sequences. (Running on oeis4.)