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A309296 (1/4) times the sum of the elements of all subsets of [n] whose sum is divisible by four.

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%I A309296 #11 Sep 09 2019 07:56:23
%S A309296 0,0,0,1,4,14,42,112,288,720,1760,4224,9984,23296,53760,122880,278528,
%T A309296 626688,1400832,3112960,6881280,15138816,33161216,72351744,157286400,
%U A309296 340787200,736100352,1585446912,3405774848,7298088960,15602810880,33285996544,70866960384
%N A309296 (1/4) times the sum of the elements of all subsets of [n] whose sum is divisible by four.
%H A309296 Alois P. Heinz, <a href="/A309296/b309296.txt">Table of n, a(n) for n = 0..1000</a>
%H A309296 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,8).
%F A309296 G.f.: -x^3*(8*x^5-4*x^4-2*x^3+2*x^2-2*x+1)/(2*x-1)^3.
%t A309296 LinearRecurrence[{6,-12,8},{0,0,0,1,4,14,42,112,288},50] (* _Harvey P. Dale_, Sep 09 2019 *)
%Y A309296 Column k=4 of A309280.
%K A309296 nonn,easy
%O A309296 0,5
%A A309296 _Alois P. Heinz_, Jul 21 2019