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%I #8 Jul 22 2019 16:42:05
%S 0,0,0,1,2,7,20,49,132,330,786,1892,4472,10368,23940,54720,123836,
%T 278664,622896,1383672,3058720,6729184,14738688,32157312,69907200,
%U 151461952,327158208,704648448,1513680192,3243601280,6934595840,14793782400,31496441856,66929938944
%N (1/6) times the sum of the elements of all subsets of [n] whose sum is divisible by six.
%H Alois P. Heinz, <a href="/A309298/b309298.txt">Table of n, a(n) for n = 0..1000</a>
%H <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 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).
%Y Column k=6 of A309280.
%K nonn,easy
%O 0,5
%A _Alois P. Heinz_, Jul 21 2019
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