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 A309295 #10 Mar 17 2023 10:32:53
%S A309295 0,0,1,4,9,30,84,202,528,1320,3144,7568,17888,41472,95760,218880,
%T A309295 495344,1114656,2491584,5534688,12234880,26916736,58954752,128629248,
%U A309295 279628800,605847808,1308632832,2818593792,6054720768,12974405120,27738383360,59175129600
%N A309295 (1/3) times the sum of the elements of all subsets of [n] whose sum is divisible by three.
%H A309295 Alois P. Heinz, <a href="/A309295/b309295.txt">Table of n, a(n) for n = 0..1000</a>
%H A309295 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,14,-36,72,-60,72,-144,104,-48,96,-64).
%F A309295 G.f.: -x^2*(8*x^8-4*x^5+8*x^4-10*x^3+3*x^2+2*x-1)/((2*x-1)^3*(2*x^3-1)^3).
%t A309295 CoefficientList[Series[-x^2(8x^8-4x^5+8x^4-10x^3+3x^2+2x-1)/((2x-1)^3(2x^3-1)^3),{x,0,40}],x] (* or *) LinearRecurrence[{6,-12,14,-36,72,-60,72,-144,104,-48,96,-64},{0,0,1,4,9,30,84,202,528,1320,3144,7568},40] (* _Harvey P. Dale_, Mar 17 2023 *)
%Y A309295 Column k=3 of A309280.
%K A309295 nonn,easy
%O A309295 0,4
%A A309295 _Alois P. Heinz_, Jul 21 2019