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A143281 Number of binary words of length n containing at least one subword 101 and no subword 11. 2
0, 0, 0, 1, 2, 4, 8, 15, 27, 48, 84, 145, 248, 421, 710, 1191, 1989, 3309, 5487, 9073, 14966, 24634, 40472, 66384, 108729, 177858, 290610, 474364, 773615, 1260643, 2052818, 3340662, 5433345, 8832432, 14351403, 23309326, 37844645, 61423513, 99663191, 161665653 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

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

a(n) = A000045(n+2)-A000930(n+2).

EXAMPLE

a(6)=8 because 8 binary words of length 6 have at least one substring 101 and no substring 11: 000101, 001010, 010100, 101000, 010101, 101010, 101001, 100101.

MAPLE

a:= n-> coeff(series(x^3/((x^2+x-1)*(x^3+x-1)), x, n+1), x, n):

seq(a(n), n=0..60);

MATHEMATICA

CoefficientList[Series[x^3/((x^2+x-1)*(x^3+x-1)), {x, 0, 50}], x] (* G. C. Greubel, Apr 28 2017 *)

PROG

(PARI) x='x+O('x^50); concat([0, 0, 0], Vec(x^3/((x^2+x-1)*(x^3+x-1)))) \\ G. C. Greubel, Apr 28 2017

CROSSREFS

Cf. A000045, A000930, first column of A143291.

Sequence in context: A222152 A000126 A182716 * A098057 A289692 A074029

Adjacent sequences:  A143278 A143279 A143280 * A143282 A143283 A143284

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 04 2008

STATUS

approved

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Last modified February 25 22:55 EST 2020. Contains 332270 sequences. (Running on oeis4.)