A381332 a(n) is the number of different hooklength lists of the plane partitions of n.

1, 1, 2, 4, 6, 11, 19, 31, 52, 86, 146, 231, 392, 615, 1006, 1594, 2612, 4062, 6518, 10116, 15958, 24557, 38565, 58548

Offset

1,3

Comments

The hooklength list of a plane partition is the sorted list of 3D hooklengths of its 3D Ferrers plot, analogous to the classic 2D case.

Links

Table of n, a(n) for n=1..24.

Wouter Meeussen, Mma functions for plane and solid partitions

Example

The plane partition {{2,1},{2}} has hooklengths {{{4,2},{1}},{{2,1}}} and so hooklength list is {4,2,2,1,1}. So a(2) = 1.
The 24 plane partitions of n=5 generate only these 6 hooklength lists: {4,2,2,1,1}, {4,3,2,1,1}, {5,2,1,1,1}, {5,2,2,1,1}, {5,3,2,1,1}, {5,4,3,2,1}. So a(5) = 6.

Mathematica

Table[Length[Union[planehooks/@planepartitions[n]]], {n, 20}]

Crossrefs

Cf. A097391, A094504, A000219, A000041.

Sequence in context: A018167 A295831 A140443 * A224957 A115992 A115993

Adjacent sequences: A381329 A381330 A381331 * A381333 A381334 A381335

Keyword

nonn,more

Author

Wouter Meeussen, Feb 20 2025

Status

approved