A368556 a(n) is the number of triangular partitions of size n with just one removable cell.

1, 2, 2, 2, 4, 2, 2, 6, 4, 2, 8, 2, 4, 10, 6, 2, 10, 6, 8, 12, 6, 2, 18, 6, 8, 16, 8, 8, 24, 2, 6, 20, 14, 12, 26, 6, 6, 24, 22, 6, 30, 6, 20, 30, 10, 8, 36, 14, 18, 32, 18, 4, 48, 18, 22, 30, 14, 12, 52, 14, 20, 42, 26, 24, 44, 6, 20, 52, 38, 12, 54, 10, 26

Offset: 1

Author

Alejandro B. Galván, Dec 29 2023

Keywords

• nonn

Links

• Sergi Elizalde and Alejandro B. Galván, Triangular partitions: enumeration, structure, and generation, arXiv:2312.16353 [math.CO], (2023).

Crossrefs

The number of triangular partitions of size n with any number of removable cells is in A352882.

Cf. A368554 (with two removable cells).

Formula

See the g.f. in Proposition 6.2. of Elizalde and Galván.