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

0,2

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).

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).

Example

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

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);

Crossrefs

Row n=3 of A238016.

Cf. A001399.

Sequence in context: A342599 A291951 A176408 * A247330 A168366 A134524

Adjacent sequences: A238627 A238628 A238629 * A238631 A238632 A238633

Keyword

nonn

Author

Alois P. Heinz, Mar 01 2014

Status

approved