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A238630 Number of partitions of 3^n into parts that are at most 3.

%I A238630 #23 Jun 26 2024 04:04:07
%S A238630 1,3,12,75,588,5043,44652,399675,3590508,32294883,290594892,
%T A238630 2615176875,23536060428,211822949523,1906401762732,17157601515675,
%U A238630 154418370594348,1389765206208963,12507886468460172,112570977053880075,1013138789998136268,9118249099522873203
%N A238630 Number of partitions of 3^n into parts that are at most 3.
%H A238630 Alois P. Heinz, <a href="/A238630/b238630.txt">Table of n, a(n) for n = 0..1000</a>
%H A238630 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (13,-39,27).
%F A238630 a(n) = [x^(3^n)] Product_{j=1..3} 1/(1-x^j).
%F A238630 G.f.: (9*x^3+12*x^2-10*x+1)/((1-x)*(1-3*x)*(1-3^2*x)).
%F A238630 a(n) = A001399(3^n) = round((3^n+3)^2/12).
%F A238630 a(n) = 3*A051500(n-1) for n>=1. - _Hugo Pfoertner_, May 04 2024
%e A238630 a(2) = 12: 333, 3222, 3321, 22221, 32211, 33111, 222111, 321111, 2211111, 3111111, 21111111, 111111111.
%p A238630 gf:= (9*x^3+12*x^2-10*x+1)/((1-x)*(1-3*x)*(1-3^2*x)):
%p A238630 a:= n-> coeff(series(gf, x, n+1), x, n):
%p A238630 seq(a(n), n=0..30);
%t A238630 Round[(3^Range[0, 25] + 3)^2/12] (* _Paolo Xausa_, Jun 26 2024 *)
%Y A238630 Row n=3 of A238016.
%Y A238630 Cf. A001399, A051500.
%K A238630 nonn
%O A238630 0,2
%A A238630 _Alois P. Heinz_, Mar 01 2014