A119266 Number of 3-dimensional partitions of n up to conjugacy.

1, 1, 1, 2, 4, 7, 13, 25, 49, 93, 181, 351, 687, 1332, 2591, 5003, 9644, 18462, 35208, 66721, 125840, 235914, 440020, 816122, 1505986, 2764303, 5048960, 9176069

Offset: 0

Author

Franklin T. Adams-Watters, May 11 2006

Keywords

• more
• nonn

Comments

Partitions are considered as generalized Ferrers diagrams; any permutation of the axes produces a conjugate.

Crossrefs

Cf. A119269, A000293.

Cf. A119338.

Cf. A096573, A096575, A382247, A096577

Formula

a(n) = (A000293(n) + 6*A096573(n) + 8*A096575(n) + 3*A382247(n) + 6*A096577(n))/24 by Burnside's lemma. - Wouter Meeussen, Mar 19 2025

Extensions

a(9)-a(23) from Max Alekseyev, May 15 2006

a(24)-a(27) from Max Alekseyev, Mar 20 2025