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 A309298 #12 Aug 01 2025 16:09:40
%S A309298 0,0,0,1,2,7,20,49,132,330,786,1892,4472,10368,23940,54720,123836,
%T A309298 278664,622896,1383672,3058720,6729184,14738688,32157312,69907200,
%U A309298 151461952,327158208,704648448,1513680192,3243601280,6934595840,14793782400,31496441856,66929938944
%N A309298 (1/6) times the sum of the elements of all subsets of [n] whose sum is divisible by six.
%H A309298 Alois P. Heinz, <a href="/A309298/b309298.txt">Table of n, a(n) for n = 0..1000</a>
%H A309298 <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 A309298 G.f.: -x^3*(96*x^16-80*x^15+8*x^14-140*x^13+112*x^12+12*x^11 +40*x^10 -36*x^9 -32*x^8 +32*x^7 -14*x^6 +20*x^5 -21*x^4+12*x^3-7*x^2 +4*x-1) / ((2*x-1)^3 *(2*x^3-1)^3).
%F A309298 a(n) = 6*a(n-1) - 12*a(n-2) + 14*a(n-3) - 36*a(n-4) + 72*a(n-5) - 60*a(n-6) + 72*a(n-7) - 144*a(n-8) + 104*a(n-9) - 48*a(n-10) + 96*a(n-11) - 64*a(n-12). - _Wesley Ivan Hurt_, Jul 23 2025
%t A309298 CoefficientList[Series[-x^3*(96*x^16 - 80*x^15 + 8*x^14 - 140*x^13 + 112*x^12 + 12*x^11 + 40*x^10 - 36*x^9 - 32*x^8 + 32*x^7 - 14*x^6 + 20*x^5 - 21*x^4 + 12*x^3 - 7*x^2 + 4*x - 1)/((2*x - 1)^3*(2*x^3 - 1)^3), {x, 0, 40}], x] (* _Wesley Ivan Hurt_, Jul 23 2025 *)
%t A309298 LinearRecurrence[{6,-12,14,-36,72,-60,72,-144,104,-48,96,-64},{0,0,0,1,2,7,20,49,132,330,786,1892,4472,10368,23940,54720,123836,278664,622896,1383672},40] (* _Harvey P. Dale_, Aug 01 2025 *)
%Y A309298 Column k=6 of A309280.
%K A309298 nonn,easy
%O A309298 0,5
%A A309298 _Alois P. Heinz_, Jul 21 2019