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A107066 Expansion of 1/(1-2x+x^5). 12
1, 2, 4, 8, 16, 31, 60, 116, 224, 432, 833, 1606, 3096, 5968, 11504, 22175, 42744, 82392, 158816, 306128, 590081, 1137418, 2192444, 4226072, 8146016, 15701951, 30266484, 58340524, 112454976, 216763936, 417825921, 805385358, 1552430192, 2992405408, 5768046880 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums of number triangle A107065.

Same as A018922 plus first 3 additional terms. - Vladimir Joseph Stephan Orlovsky, Jul 08 2011

a(n) is the number of binary words of length n containing no subword 01011. - Alois P. Heinz, Mar 14 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

T. Langley, J. Liese, J. Remmel, Generating Functions for Wilf Equivalence Under Generalized Factor Order , J. Int. Seq. 14 (2011) # 11.4.2

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

FORMULA

a(n) = 2a(n-1)-a(n-5); a(n) = sum{k=0..floor(n/5), C(n-4k, k)2^(n-2k)(-1)^k}.

a(n) = A018922(n-3) for n>=3. - R. J. Mathar, Mar 09 2007

First difference of A119407. - Michael Somos, Dec 28 2012

EXAMPLE

1 + 2*x + 4*x^2 + 8*x^3 + 16*x^4 + 31*x^5 + 60*x^6 + 116*x^7 + 224*x^8 + ...

MATHEMATICA

CoefficientList[Series[1/(1 - 2*z + z^5), {z, 0, 100}], z] (* Vladimir Joseph Stephan Orlovsky, Jul 08 2011 *)

PROG

(PARI) {a(n) = if( n<0, n = -n; polcoeff( -x^5 / (1 - 2*x^4 + x^5) + x * O(x^n), n), polcoeff( 1 / (1 - 2*x + x^5) + x * O(x^n), n))} /* Michael Somos, Dec 28 2012 */

CROSSREFS

Cf. A018922, A119407.

Cf. A209888. - Alois P. Heinz, Mar 14 2012

Sequence in context: A189075 A189077 A118891 * A141019 A210003 A209888

Adjacent sequences:  A107063 A107064 A107065 * A107067 A107068 A107069

KEYWORD

easy,nonn

AUTHOR

Paul Barry, May 10 2005

STATUS

approved

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Last modified April 20 14:27 EDT 2019. Contains 322310 sequences. (Running on oeis4.)