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A052922 Expansion of 1/(1 - 2*x^3 - x^4). 1

%I

%S 1,0,0,2,1,0,4,4,1,8,12,6,17,32,24,40,81,80,104,202,241,288,508,684,

%T 817,1304,1876,2318,3425,5056,6512,9168,13537,18080,24848,36242,49697,

%U 67776,97332,135636,185249,262440,368604,506134,710129,999648,1380872

%N Expansion of 1/(1 - 2*x^3 - x^4).

%H G. C. Greubel, <a href="/A052922/b052922.txt">Table of n, a(n) for n = 0..1000</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=907">Encyclopedia of Combinatorial Structures 907</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,1).

%F G.f.: 1/(1 - 2*x^3 - x^4).

%F a(n) = 2*a(n-3) + a(n-4), with a(0)=1, a(1)=0, a(2)=0, a(3)=2.

%F a(n) = Sum_{alpha=RootOf(-1+2*z^3+z^4)} (1/86)*(4 +26*alpha -3*alpha^2 -6*alpha^3)*alpha^(-1-n).

%p spec := [S,{S=Sequence(Prod(Z,Z,Union(Z,Z,Prod(Z,Z))))},unlabeled]: seq(combstruct[count](spec,size=n), n=0..50);

%p seq(coeff(series(1/(1 -2*x^3 -x^4), x, n+1), x, n), n = 0..50); # _G. C. Greubel_, Oct 16 2019

%t LinearRecurrence[{0,0,2,1}, {1,0,0,2}, 50] (* _G. C. Greubel_, Oct 16 2019 *)

%o (PARI) my(x='x+O('x^50)); Vec(1/(1 -2*x^3 -x^4)) \\ _G. C. Greubel_, Oct 16 2019

%o (MAGMA) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1 -2*x^3 -x^4) )); // _G. C. Greubel_, Oct 16 2019

%o (Sage)

%o def A052922_list(prec):

%o P.<x> = PowerSeriesRing(ZZ, prec)

%o return P(1/(1 -2*x^3 -x^4)).list()

%o A052922_list(50) # _G. C. Greubel_, Oct 16 2019

%o (GAP) a:=[1,0,0,2];; for n in [5..50] do a[n]:=2*a[n-3]+a[n-4]; od; a; # _G. C. Greubel_, Oct 16 2019

%K easy,nonn

%O 0,4

%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000

%E More terms from _James A. Sellers_, Jun 05 2000

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Last modified May 31 02:51 EDT 2020. Contains 334747 sequences. (Running on oeis4.)