A105369 - OEIS

%I #10 Sep 08 2019 01:56:12

%S 1,-2,3,-5,10,-20,35,-50,50,0,-175,625,-1625,3625,-7250,13125,-21250,

%T 29375,-29375,0,106250,-384375,1006250,-2250000,4500000,-8140625,

%U 13171875,-18203125,18203125,0,-65859375,238281250,-623828125,1394921875,-2789843750,5046875000,-8166015625

%N Expansion of ((1+x)^3 - x^3)/((1+x)^5 - x^5).

%C Consecutive pair sums gives A105370.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-5,-10,-10,-5)

%F G.f.: (1 + 3*x + 3*x^2)/(1 + 5*x + 10*x^2 + 10*x^3 + 5*x^4);

%F a(n) = 2*sqrt(5)*(5/2 - sqrt(5)/2)^(n/2)*cos(7*Pi*n/10 + Pi/5)/5 + 2*sqrt(5)*(5/2 + sqrt(5)/2)^(n/2)*cos(9*Pi*n/10 + 2*Pi*/5)/5.

%K easy,sign

%O 0,2

%A _Paul Barry_, Apr 01 2005