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A096419
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Number of cyclically symmetric plane partitions (Macdonald's plane partition conjecture).
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4
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,7
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COMMENTS
| Equals A048141 (C3v symmetry) + 2* A048142 (only C3 symmetry).
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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.
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LINKS
| Wouter Meeussen, Table of n, a(n) for n=1..151
Eric Weisstein's World of Mathematics, Macdonald's Plane Partition Conjecture
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FORMULA
| See Mathematica code for a formula.
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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]
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CROSSREFS
| Cf. A047993, A048141, A048142.
Sequence in context: A025841 A138468 A029296 * A130182 A024361 A190676
Adjacent sequences: A096416 A096417 A096418 * A096420 A096421 A096422
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KEYWORD
| nonn
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AUTHOR
| Wouter Meeussen (wouter.meeussen(AT)pandora.be), Aug 08 2004
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