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A008806 Expansion of (1+x^3)/((1-x^2)^2*(1-x^3)). 2
1, 0, 2, 2, 3, 4, 6, 6, 9, 10, 12, 14, 17, 18, 22, 24, 27, 30, 34, 36, 41, 44, 48, 52, 57, 60, 66, 70, 75, 80, 86, 90, 97, 102, 108, 114, 121, 126, 134, 140, 147, 154, 162, 168, 177, 184, 192, 200, 209, 216, 226, 234, 243, 252, 262, 270, 281, 290, 300, 310, 321 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

David Beckwith, Vadim Ponomarenko and Rob Pratt, Building Two Piles of Equal Height: 11183, The American Mathematical Monthly, 114 (2007), 551-552.

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

FORMULA

From R. J. Mathar, Nov 08 2010: (Start)

a(n) = (16*A131713(n) +29 +24*n +6*n^2 +27*(-1)^n)/72.

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

a(n) = floor((6*n^2+24*n+61+27*(-1)^n)/72). - Tani Akinari, Jul 24 2013

MAPLE

seq(coeff(series((1+x^3)/((1-x^2)^2*(1-x^3)), x, n+1), x, n), n = 0..70); # G. C. Greubel, Sep 12 2019

MATHEMATICA

CoefficientList[Series[(1+x^3)/((1-x^2)^2*(1-x^3)), {x, 0, 70}], x] (* or *) LinearRecurrence[{1, 1, 0, -1, -1, 1}, {1, 0, 2, 2, 3, 4}, 70] (* G. C. Greubel, Sep 12 2019 *)

PROG

(PARI) Vec((1+x^3)/((1-x^2)^2*(1-x^3)) +O(x^70)) \\ Charles R Greathouse IV, Sep 26 2012; modified by G. C. Greubel, Sep 12 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( (1+x^3)/((1-x^2)^2*(1-x^3)) )); // G. C. Greubel, Sep 12 2019

(Sage)

def A008806_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P((1+x^3)/((1-x^2)^2*(1-x^3))).list()

A008806_list(70) # G. C. Greubel, Sep 12 2019

(GAP) a:=[1, 0, 2, 2, 3, 4];; for n in [7..70] do a[n]:=a[n-1]+a[n-2]-a[n-4]-a[n-5]+a[n-6]; od; a; # G. C. Greubel, Sep 12 2019

CROSSREFS

Sequence in context: A152048 A046934 A093594 * A238860 A144367 A075465

Adjacent sequences:  A008803 A008804 A008805 * A008807 A008808 A008809

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Terms a(52) onward added by G. C. Greubel, Sep 12 2019

STATUS

approved

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Last modified November 20 17:09 EST 2019. Contains 329337 sequences. (Running on oeis4.)