A112523 - OEIS

%I #14 Jan 12 2022 09:00:24

%S 0,1,3,-8,-17,35,72,-145,-291,584,1169,-2339,-4680,9361,18723,-37448,

%T -74897,149795,299592,-599185,-1198371,2396744,4793489,-9586979,

%U -19173960,38347921,76695843,-153391688,-306783377,613566755,1227133512,-2454267025,-4908534051,9817068104

%N Expansion of x*(1+3*x-4*x^2-5*x^3-4*x^6+4*x^5+3*x^4) / ((1+4*x^2)*(1+x^2)*(1-x^2+x^4)).

%H Colin Barker, <a href="/A112523/b112523.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 (0,-4,0,0,0,-1,0,-4).

%F a(n) = -4*a(n-2) - a(n-6) - 4*a(n-8). - _Colin Barker_, May 18 2019

%t LinearRecurrence[{0,-4,0,0,0,-1,0,-4}, {0,1,3,-8,-17,35,72,-145,-291}, 40] (* _G. C. Greubel_, Jan 12 2022 *)

%o (PARI) my(x='x+O('x^40)); concat([0], Vec(x*(1+3*x-4*x^2-5*x^3-4*x^6+4*x^5+3*x^4)/((1+4*x^2)*(1+x^2)*(1-x^2+x^4)))) \\ _Charles R Greathouse IV_, Sep 27 2012

%o (Sage)

%o def A112523_list(prec):

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

%o     return P( x*(1+3*x-4*x^2-5*x^3-4*x^6+4*x^5+3*x^4)/((1+4*x^2)*(1+x^2)*(1-x^2+x^4)) ).list()

%o A112523_list(40) # _G. C. Greubel_, Jan 12 2022

%o (Magma)

%o R<x>:=PowerSeriesRing(Rationals(), 40);

%o [0] cat Coefficients(R!( x*(1+3*x-4*x^2-5*x^3-4*x^6+4*x^5+3*x^4)/((1+4*x^2)*(1+x^2)*(1-x^2+x^4)) )); // _G. C. Greubel_, Jan 12 2022

%Y Cf. A112522.

%K sign,easy

%O 0,3

%A _Creighton Dement_, Sep 09 2005