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

1,3

Comments

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

Links

Table of n, a(n) for n=1..37.

Example

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.

Sequence in context: A032254 A323586 A048237 * A357239 A071085 A240951

Adjacent sequences: A048136 A048137 A048138 * A048140 A048141 A048142

Keyword

nonn

Author

Wouter Meeussen

Extensions

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

Status

approved