A392637 Number of planar partitions of n with strictly decreasing columns and where parts decrease by at most 1 along each row.

1, 1, 1, 2, 3, 4, 6, 9, 12, 17, 24, 32, 44, 60, 80, 107, 143, 188, 248, 326, 425, 553, 718, 926, 1193, 1533, 1961, 2503, 3189, 4047, 5127, 6481, 8170, 10278, 12907, 16169, 20219, 25238, 31440, 39098, 48545, 60163, 74447, 91982, 113467, 139764, 171918, 211159, 259011, 317291, 388172

Offset

0,4

Comments

Also, the ranking of the lattice of totally symmetric plane partitions ordered by containment.

Equivalently, a(n) is the number of totally symmetric plane partitions with n orbits of cubes up to the action of S_3.

Links

Table of n, a(n) for n=0..50.

Formula

G.f.: Product_{k>=1} (1 - x^(6*k-4)) / (1 - x^k)^ceiling(k/6).

Example

The a(8) = 12 plane partitions of 8 with strictly decreasing columns and where parts decrease by at most 1 along each row:
  3221       32111      22211      221111     2111111    11111111
.
  3211       2221       22111      211111     321        2211
  1          1          1          1          11         11

Crossrefs

Cf. A000219, A003293, A005157, A392511.

Sequence in context: A036003 A027338 A064174 * A062121 A094995 A375980

Adjacent sequences: A392634 A392635 A392636 * A392638 A392639 A392640

Keyword

nonn

Author

Ludovic Schwob, Feb 16 2026

Status

approved