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A309299 (1/7) times the sum of the elements of all subsets of [n] whose sum is divisible by seven.

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%I A309299 #7 Jul 22 2019 18:57:02
%S A309299 0,0,0,0,2,5,15,40,97,237,571,1385,3263,7618,17580,40146,90962,204618,
%T A309299 457446,1016494,2247000,4943400,10828248,23625120,51358776,111277576,
%U A309299 240359368,517697136,1112090144,2383049792,5094795600,10868896688,23140232368,49172993152
%N A309299 (1/7) times the sum of the elements of all subsets of [n] whose sum is divisible by seven.
%H A309299 Alois P. Heinz, <a href="/A309299/b309299.txt">Table of n, a(n) for n = 0..1000</a>
%H A309299 <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,8,0,0,0,6,-36,72,-48,0,0,0,-12,72,-144,96,0,0,0,8,-48,96,-64).
%F A309299 G.f.: -x^4*(8*x^18+24*x^14-12*x^12+4*x^11+16*x^10-38*x^9+49*x^8 -15*x^7 +7*x^6 -15*x^5 +3*x^4 +6*x^3 -9*x^2+7*x-2) / ((2*x-1)^3 *(2*x^7-1)^3).
%Y A309299 Column k=7 of A309280.
%K A309299 nonn,easy
%O A309299 0,5
%A A309299 _Alois P. Heinz_, Jul 21 2019