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
Keywords
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
Programs
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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.
Comments