%I #11 Jun 21 2022 14:16:52
%S 6,9,17,39,101,279,797,2319,6821,20199,60077,179199,535541,1602519,
%T 4799357,14381679,43112261,129271239,387682637,1162785759,3487832981,
%U 10462450359,31385253917,94151567439,282446313701,847322163879,2541932937197,7625731702719
%N Total sum of n-th powers of parts in all partitions of 3.
%H Alois P. Heinz, <a href="/A229354/b229354.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6).
%F a(n) = Sum_{k=1..3} A066633(3,k) * k^n.
%F a(n) = 4 + 2^n + 3^n.
%F G.f.: -(29*x^2-27*x+6)/((x-1)*(2*x-1)*(3*x-1)).
%p a:= n-> 4+2^n+3^n:
%p seq(a(n), n=0..30);
%t LinearRecurrence[{6,-11,6},{6,9,17},30] (* _Harvey P. Dale_, Jun 21 2022 *)
%Y Row n=3 of A213191.
%K nonn,easy
%O 0,1
%A _Alois P. Heinz_, Sep 20 2013