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A118898 Number of binary sequences of length n containing exactly one subsequence 0000. 2
0, 0, 0, 0, 1, 2, 5, 12, 28, 62, 136, 294, 628, 1328, 2787, 5810, 12043, 24840, 51016, 104380, 212848, 432732, 877400, 1774672, 3581605, 7213746, 14502449, 29106100, 58323844, 116702074, 233199000, 465405058, 927744428, 1847359520, 3674769991 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Column 1 of A118897.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (2,1,0,-1,-4,-3,-2,-1).

FORMULA

G.f.=z^4/(1-z-z^2-z^3-z^4)^2.

Contribution from Bobby Milazzo, Aug 30 2009: (Start)

a(1)=0,a(2)=0,a(3)=0,a(4)=1,a(5)=2,a(6)=5,a(7)=12,a(8)=28

a(n)=2a(n-1)+a(n-2)-a(n-4)-4a(n-5)-3a(n-6)-2a(n-7)-a(n-8) (End)

EXAMPLE

a(6)=5 because we have 000010,000011,010000,100001 and 110000.

G.f. = x^4 + 2*x^5 + 5*x^6 + 12*x^7 + 28*x^8 + 62*x^9 + ... - Zerinvary Lajos, Jun 02 2009

MAPLE

g:=z^4/(1-z-z^2-z^3-z^4)^2: gser:=series(g, z=0, 40): seq(coeff(gser, z, n), n=0..37);

MATHEMATICA

Contribution from Bobby Milazzo, Aug 30 2009: (Start)

With Mathematica 7.01

RecurrenceTable[{a[1]==0, a[2]==0, a[3]==0, a[4]==1, a[5]==2, a[6]==5,

a[7]==12, a[8]==28, a[n]==2a[n-1]+a[n-2]-a[n-4]-4a[n-5]

-3a[n-6]-2a[n-7]-a[n-8]}, a, {n, 9, 50}] (End)

LinearRecurrence[{2, 1, 0, -1, -4, -3, -2, -1}, {0, 0, 0, 0, 1, 2, 5, 12}, 50] (* Harvey P. Dale, Aug 01 2012 *)

PROG

(Sage) taylor( mul(x/(1-x-x^2-x^3-x^4)^2 for i in xrange(1, 2)), x, 0, 31)# Zerinvary Lajos, Jun 02 2009

CROSSREFS

Cf. A118897.

Sequence in context: A171579 A228638 A202604 * A111586 A192657 A320590

Adjacent sequences:  A118895 A118896 A118897 * A118899 A118900 A118901

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, May 04 2006

STATUS

approved

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Last modified November 12 16:50 EST 2018. Contains 317116 sequences. (Running on oeis4.)