%I #17 Mar 20 2025 13:53:52

%S 1,1,1,2,4,7,13,25,49,93,181,351,687,1332,2591,5003,9644,18462,35208,

%T 66721,125840,235914,440020,816122,1505986,2764303,5048960,9176069

%N Number of 3-dimensional partitions of n up to conjugacy.

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

%F 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

%Y Cf. A119269, A000293.

%Y Cf. A119338.

%Y Cf. A096573, A096575, A382247, A096577

%K more,nonn

%O 0,4

%A _Franklin T. Adams-Watters_, May 11 2006

%E a(9)-a(23) from _Max Alekseyev_, May 15 2006

%E a(24)-a(27) from _Max Alekseyev_, Mar 20 2025