A144701 - OEIS

%I #12 Jun 16 2022 02:01:34

%S 1,-9,26,-25,-36,133,-132,-81,375,-374,-144,806,-805,-225,1480,-1479,

%T -324,2451,-2450,-441,3773,-3772,-576,5500,-5499,-729,7686,-7685,-900,

%U 10385,-10384,-1089,13651,-13650,-1296,17538,-17537

%N Hankel transform of expansion of 1/c(x)^3, c(x) the g.f. of A000108.

%C Hankel transform of A115142.

%H G. C. Greubel, <a href="/A144701/b144701.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (-4,-10,-16,-19,-16,-10,-4,-1).

%F G.f.: (1+x)*(1-x)*(1-5*x+x^2)/(1+x+x^2)^4.

%F a(n) = (6 - 7*n - 9*n^2 - 2*n^3)*cos(2*Pi*n/3)/6 - sqrt(3)*(42 + 55*n + 21*n^2 + 2*n^3)*sin(2*Pi*n/3)/18.

%t LinearRecurrence[{-4,-10,-16,-19,-16,-10,-4,-1}, {1,-9,26,-25,-36,133,-132,-81}, 40] (* _G. C. Greubel_, Jun 16 2022 *)

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x^2)*(1-5*x+x^2)/(1+x+x^2)^4 )); // _G. C. Greubel_, Jun 16 2022

%o (SageMath)

%o def A144701_list(prec):

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

%o     return P( (1-x^2)*(1-5*x+x^2)/(1+x+x^2)^4 ).list()

%o A144701_list(40) # _G. C. Greubel_, Jun 16 2022

%Y Cf. A000108, A099504, A115142, A128504.

%K easy,sign

%O 0,2

%A _Paul Barry_, Sep 19 2008