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A309301 (1/9) times the sum of the elements of all subsets of [n] whose sum is divisible by nine.

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%I A309301 #16 Apr 20 2023 14:49:46
%S A309301 0,0,0,0,1,3,9,23,60,150,354,843,1983,4608,10638,24318,55043,123862,
%T A309301 276868,614996,1359446,2990726,6550528,14292132,31069860,67316446,
%U A309301 145403700,313177200,672746880,1441600632,3082042512,6575014400,13998418584,29746639512
%N A309301 (1/9) times the sum of the elements of all subsets of [n] whose sum is divisible by nine.
%H A309301 Alois P. Heinz, <a href="/A309301/b309301.txt">Table of n, a(n) for n = 0..1000</a>
%H A309301 <a href="/index/Rec#order_39">Index entries for linear recurrences with constant coefficients</a>, signature (6, -12, 14, -36, 72, -60, 72, -144, 110, -84, 168, -148, 216, -432, 360, -432, 864, -636, 360, -720, 552, -432, 864, -720, 864, -1728, 1256, -624, 1248, -880, 288, -576, 480, -576, 1152, -832, 384, -768, 512).
%F A309301 G.f.: -x^4*(64*x^33-160*x^30+32*x^29+80*x^28+216*x^27+96*x^26 -312*x^25 -160*x^24 -200*x^23 +376*x^22+40*x^21 -4*x^20+164*x^19-48*x^18 +60*x^17 -516*x^16 +114*x^15+4*x^14+340*x^13-79*x^12-30*x^11-78*x^10 +4*x^9 +45*x^8 -33*x^7+20*x^6-24*x^5+24*x^4-9*x^3+3*x^2 -3*x+1) / ((2*x-1)^3 *(2*x^3-1)^3 *(2*x^9-1)^3).
%Y A309301 Column k=9 of A309280.
%K A309301 nonn,easy
%O A309301 0,6
%A A309301 _Alois P. Heinz_, Jul 21 2019