%I #16 Mar 19 2020 13:05:07

%S 0,2,3,8,5,12,7,16,9,20,11,24,13,28,15,32,17,36,19,40,21,44,23,48,25,

%T 52,27,56,29,60,31,64,33,68,35,72,37,76,39,80,41,84,43,88,45,92,47,96,

%U 49,100,51,104,53,108,55,112,57,116,59,120

%N Partial sums of A296069.

%H Colin Barker, <a href="/A296070/b296070.txt">Table of n, a(n) for n = 1..1000</a>

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

%F From _Colin Barker_, Mar 19 2020: (Start)

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

%F a(n) = 2*a(n-2) - a(n-4) for n>6.

%F a(n) = (3 + (-1)^n)*n / 2 for n>2.

%F (End)

%t Accumulate@ Nest[Append[#, Block[{k = 1, s = 1}, While[Nand[FreeQ[#, s k], And[IntegerQ@ Mean@ #, Total@ # != 0] &@ Append[#, s k]], If[s == 1, s = -1, k++; s = 1]]; s k]] &, {0}, 59] (* _Michael De Vlieger_, Dec 12 2017 *)

%o (PARI) concat(0, Vec(x^2*(2 + 3*x + 4*x^2 - x^3 - 2*x^4) / ((1 - x)^2*(1 + x)^2) + O(x^80))) \\ _Colin Barker_, Mar 19 2020

%Y Cf. A296069.

%K nonn,easy

%O 1,2

%A _Enrique Navarrete_, Dec 04 2017