A048139 Number of planar partitions of n, when partitions that are rotations of each other (when regarded as 3-D objects) are counted only once.

1, 1, 2, 5, 8, 16, 30, 54, 94, 168, 287, 493, 831, 1391, 2293, 3769, 6114, 9867, 15782, 25098, 39598, 62165, 96935, 150398, 232021, 356261, 544220, 827758, 1253222, 1889655, 2837455, 4244505, 6324993, 9392009, 13897056, 20494991, 30126628

Offset: 1

Author

Wouter Meeussen

Keywords

• nonn

Comments

Plane partitions seen as 3-dimensional-objects can have a threefold symmetry axis.

Examples

			n=3 gives 2 forms: {{3}}={{1,1,1}}={{1},{1},{1}} and {{2,1}}={{1,1},{1}}={{2},{1}}.
		

Crossrefs

Equals Cs + 2 C1 + 2 C3 + C3v, Cs=A000784, C1=A000785, C3=A048142, C3v=A048141. Cf. A000219, A005987.

Or, equals (2*A048141+A000219+4*A048142)/3.

Extensions

Edited by N. J. A. Sloane, Oct 26 2008 at the suggestion of R. J. Mathar.