This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A296070 #16 Mar 19 2020 13:05:07 %S A296070 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 A296070 52,27,56,29,60,31,64,33,68,35,72,37,76,39,80,41,84,43,88,45,92,47,96, %U A296070 49,100,51,104,53,108,55,112,57,116,59,120 %N A296070 Partial sums of A296069. %H A296070 Colin Barker, <a href="/A296070/b296070.txt">Table of n, a(n) for n = 1..1000</a> %H A296070 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1). %F A296070 From _Colin Barker_, Mar 19 2020: (Start) %F A296070 G.f.: x^2*(2 + 3*x + 4*x^2 - x^3 - 2*x^4) / ((1 - x)^2*(1 + x)^2). %F A296070 a(n) = 2*a(n-2) - a(n-4) for n>6. %F A296070 a(n) = (3 + (-1)^n)*n / 2 for n>2. %F A296070 (End) %t A296070 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 A296070 (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 A296070 Cf. A296069. %K A296070 nonn,easy %O A296070 1,2 %A A296070 _Enrique Navarrete_, Dec 04 2017