A387996 One third the number of solid partitions of n with 3 parts.

2, 2, 5, 7, 10, 13, 18, 21, 27, 32, 38, 44, 52, 58, 67, 75, 84, 93, 104, 113, 125, 136, 148, 160, 174, 186, 201, 215, 230, 245, 262, 277, 295, 312, 330, 348, 368, 386, 407, 427, 448, 469, 492, 513, 537, 560, 584, 608, 634, 658, 685, 711, 738, 765, 794, 821, 851

Offset

3,1

Links

Table of n, a(n) for n=3..59.

Formula

G.f.: q^3 * (q^2 + 2)/((1-q) * (1-q^2) * (1-q^3)).

Example

a(6) = 7 counts the 21 solid partitions of 6: 9 arrangements of the parts (3,2,1), 6 arrangements of (4,1,1), and 6 arrangements of (2,2,2).

Prog

(PARI)
A_q(N) = {Vec( q^3 * (q^2 + 2)/((1-q) * (1-q^2) * (1-q^3)) + O('q^(N+1)))}

Crossrefs

3*a(n) is column k=3 of A380893.

Cf. A000219, A000293, A002836, A207542, A379277.

Sequence in context: A308842 A241761 A278388 * A239737 A262883 A308908

Adjacent sequences: A387993 A387994 A387995 * A387997 A387998 A387999

Keyword

nonn,easy

Author

John Tyler Rascoe, Oct 13 2025

Status

approved