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Search: id:A056940
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| A056940 |
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Number of antichains (or order ideals) in the poset 4*m*n or plane partitions with rows <= m, columns <= n and entries <= 4 |
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9
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| 1, 1, 1, 1, 5, 1, 1, 15, 15, 1, 1, 35, 105, 35, 1, 1, 70, 490, 490, 70, 1, 1, 126, 1764, 4116, 1764, 126, 1, 1, 210, 5292, 24696, 24696, 5292, 210, 1, 1, 330, 13860, 116424, 232848, 116424, 13860, 330, 1, 1, 495, 32670, 457380, 1646568, 1646568, 457380
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Determinants of 4 X 4 subarrays of Pascal's triangle A007318 (a matrix entry being set to 0 when not present). - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Feb 24 2005
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REFERENCES
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Berman and Koehler, Cardinalities of finite distributive lattices, Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), p. 103-124
P. A. MacMahon, Combinatory Analysis, sect 495, 1916.
R. P. Stanley, Theory and application of plane partitions. II. Studies in Appl. Math. 50 (1971), p. 259-279. Thm. 18.1
Paul Barry, On Integer-Sequence-Based Constructions of Generalized Pascal Triangles, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.4.
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LINKS
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P. A. MacMahon, Combinatory analysis.
Index entries for sequences related to posets
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FORMULA
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Product[ C(n+m+k, m+k)/C(n+k, k), {k, 0, 3} ].
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CROSSREFS
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Cf. A000372, A056932, A001263, A056939, A056941.
Antidiagonals sum to A005362 (Hoggatt sequence)
Sequence in context: A008957 A136267 A109960 this_sequence A157523 A141691 A157147
Adjacent sequences: A056937 A056938 A056939 this_sequence A056941 A056942 A056943
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu)
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