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

1, 3, 12, 75, 588, 5043, 44652, 399675, 3590508, 32294883, 290594892, 2615176875, 23536060428, 211822949523, 1906401762732, 17157601515675, 154418370594348, 1389765206208963, 12507886468460172, 112570977053880075, 1013138789998136268, 9118249099522873203

Offset: 0

Author

Alois P. Heinz, Mar 01 2014

Keywords

• nonn

Examples

			a(2) = 12: 333, 3222, 3321, 22221, 32211, 33111, 222111, 321111, 2211111, 3111111, 21111111, 111111111.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (13,-39,27).

Crossrefs

Row n=3 of A238016.

Cf. A001399, A051500.

Programs

Maple

gf:= (9*x^3+12*x^2-10*x+1)/((1-x)*(1-3*x)*(1-3^2*x)):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..30);

Mathematica

Round[(3^Range[0, 25] + 3)^2/12] (* Paolo Xausa, Jun 26 2024 *)

Formula

a(n) = [x^(3^n)] Product_{j=1..3} 1/(1-x^j).

G.f.: (9*x^3+12*x^2-10*x+1)/((1-x)*(1-3*x)*(1-3^2*x)).

a(n) = A001399(3^n) = round((3^n+3)^2/12).

a(n) = 3*A051500(n-1) for n>=1. - Hugo Pfoertner, May 04 2024