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

1,7

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

Formula

See Mathematica code for a formula.

Mathematica

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}]/.m->50, {q, 0, 97}], q]

Crossrefs

Cf. A047993, A048141, A048142.

Sequence in context: A138468 A337548 A029296 * A283616 A130182 A024361

Adjacent sequences: A096416 A096417 A096418 * A096420 A096421 A096422

Keyword

nonn

Author

Wouter Meeussen, Aug 08 2004

Status

approved