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

Author

Wouter Meeussen, Feb 20 2025

Keywords

• nonn
• more

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.

Examples

			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.
		

Links

• Wouter Meeussen, Mma functions for plane and solid partitions

Crossrefs

Cf. A097391, A094504, A000219, A000041.

Programs

Mathematica

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