A048142 Number of symmetrical planar partitions of n: planar partitions (A000219) that when regarded as 3-D objects have only a threefold axis of symmetry, i.e., C3 symmetry.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 2, 2, 0, 3, 3, 0, 5, 6, 0, 7, 9, 0, 11, 16, 1, 14, 23, 2, 20, 36, 4, 27, 52, 7, 37, 78, 13, 48, 111, 21, 65, 163, 36, 83, 227, 56, 109, 322, 89, 139, 444, 135, 179, 618, 207, 226, 841, 305, 288, 1151, 453, 361

Offset: 1

Author

Wouter Meeussen

Keywords

• nice
• nonn

Comments

Only one of the pair left-handed, right-handed, is enumerated.

Examples

			The plane partitions {{3, 2, 2}, {3, 1}, {1, 1}} and {{3, 2, 2}, {3, 2}, {1, 1}} have C3 symmetry.
		

Links

• Wouter Meeussen, Table of n, a(n) for n = 1..202

Crossrefs

Cf. A000219, A000784, A000785, A000786, A005987, A048141, A051056-A051061, A096419.

Formula

a(n) = (A096419(n) - A048141(n))/2.