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A276785 Number of binary strings of length n containing the substring 11011. 2
0, 0, 0, 0, 0, 1, 4, 12, 31, 75, 175, 399, 894, 1975, 4313, 9330, 20026, 42704, 90558, 191117, 401654, 841016, 1755249, 3652663, 7581369, 15698735, 32438224, 66897295, 137718495, 283056086, 580906268, 1190538424, 2436854280, 4982012329, 10174319500, 20756971236, 42306806495, 86153127395 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Table of n, a(n) for n=0..37.

Aashir Shukla et al., How many Binary Strings of length N contain within it the substring '11011'?, Math Stack Exchange, circa Sep 09 2016

FORMULA

G.f.: 1/(1-2*x) - (1+x^3+x^4)/(1-2*x+x^3-x^4-x^5) = x^5/((-1+2*x)*(x^5+x^4-x^3+2*x-1)).

Equals 2^n - A210021(n).

a(n) = Sum_{k>0} A277678(n,k). - Alois P. Heinz, Oct 26 2016

CROSSREFS

Cf. A210021, A277678.

Sequence in context: A232580 A133546 A190376 * A171844 A324971 A273387

Adjacent sequences:  A276782 A276783 A276784 * A276786 A276787 A276788

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Oct 05 2016, following a suggestion from Rick L. Shepherd

STATUS

approved

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Last modified May 22 18:53 EDT 2019. Contains 323481 sequences. (Running on oeis4.)