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A238630 Number of partitions of 3^n into parts that are at most 3. 2
1, 3, 12, 75, 588, 5043, 44652, 399675, 3590508, 32294883, 290594892, 2615176875, 23536060428, 211822949523, 1906401762732, 17157601515675, 154418370594348, 1389765206208963, 12507886468460172, 112570977053880075, 1013138789998136268, 9118249099522873203 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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

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Last modified July 31 01:15 EDT 2021. Contains 346365 sequences. (Running on oeis4.)