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A133262
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Number of two-dimensional simple permutations.
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0
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1, 4, 8, 172, 5204, 222716, 12509188, 889421564, 78097622276, 8312906703868, 1056520142488580, 158263730949406716, 27626236450406776836, 5563092167972597137404, 1280742543230231763615748, 334405228960123174787678204, 98317121153947856929753989124, 32339023133437156084762282819580, 11831483864832785151824395066146820, 4789379698138059405310741712024371196
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OFFSET
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1,2
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COMMENTS
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A two-dimensional permutation of n is a vector of three permutations, with the first element being the identity permutation. For example, ( (1 2 3) (1 3 2) (3 1 2) ) is a two-dimensional permutation of 3. The example is a simple two-dimensional permutation because none of the intervals of length 2 in the permutations is common among all three. On the other hand, ( (1 2 3) (1 3 2) (2 3 1) ) is not simple because the intervals covering 2 and 3 are common among all three permutations.
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LINKS
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Table of n, a(n) for n=1..20.
M. H. Albert, M. D. Atkinson and M. Klazar, The enumeration of simple permutations, Journal of Integer Sequences 6 (2003), Article 03.4.4.
Hao Zhang and Daniel Gildea, Enumeration of Factorizable Multi-Dimensional Permutations, J. Integer Sequences 10 (2007), Article 07.5.8.
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CROSSREFS
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Cf. A006318, A111111.
Sequence in context: A330860 A264510 A188268 * A120822 A013065 A013096
Adjacent sequences: A133259 A133260 A133261 * A133263 A133264 A133265
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KEYWORD
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nonn
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AUTHOR
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Hao Zhang and Daniel Gildea (zhanghao(AT)cs.rochester.edu), Oct 15 2007
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EXTENSIONS
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More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 10 2008
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STATUS
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approved
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