login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Partial sums of A296069.
2

%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