A096419 Number of cyclically symmetric plane partitions (Macdonald's plane partition conjecture).

1, 0, 0, 1, 0, 0, 2, 1, 0, 2, 1, 0, 4, 3, 0, 5, 4, 0, 8, 8, 0, 10, 11, 0, 15, 19, 1, 20, 27, 1, 28, 43, 3, 36, 61, 6, 50, 92, 11, 64, 129, 18, 86, 189, 33, 110, 262, 51, 145, 374, 84, 184, 514, 129, 238, 718, 201, 300, 977, 300, 384, 1344, 454, 482, 1812, 661, 609, 2459, 972

Offset: 1

Author

Wouter Meeussen, Aug 08 2004

Keywords

• nonn

Comments

Equals A048141 (C3v symmetry) + 2* A048142 (only C3 symmetry).

References

• Andrews, G. E. "Plane Partitions (III): The Weak Macdonald Conjecture." Invent. Math. 53, 193-225, 1979.
• Mills, W. H.; Robbins, D. P.; and Rumsey, H. Jr., Proof of the Macdonald Conjecture. Invent. Math. 66, 73-87, 1982.

Links

• Wouter Meeussen, Table of n, a(n) for n=1..151
• Eric Weisstein's World of Mathematics, Macdonald's Plane Partition Conjecture

Crossrefs

Cf. A047993, A048141, A048142.

Programs

Mathematica

len=151;m=Ceiling[len/3];mcdon=Rest@CoefficientList[Series[Product[(1-q^(3i-1))/(1-q^(3i-2)) Product[(1-q^(3(m+i+j-1)))/(1-q^(3(2i+j-1))), {j, i, m}], {i, 1, m}], {q, 0, len}], q] (* updated by Wouter Meeussen, Apr 15 2025 *)

Formula

See Mathematica code for a formula.