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 A133262 Number of two-dimensional simple permutations. 0
 1, 4, 8, 172, 5204, 222716, 12509188, 889421564, 78097622276, 8312906703868, 1056520142488580, 158263730949406716, 27626236450406776836, 5563092167972597137404, 1280742543230231763615748, 334405228960123174787678204, 98317121153947856929753989124, 32339023133437156084762282819580, 11831483864832785151824395066146820, 4789379698138059405310741712024371196 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS 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. CROSSREFS Cf. A006318, A111111. Sequence in context: A330860 A264510 A188268 * A120822 A013065 A013096 Adjacent sequences: A133259 A133260 A133261 * A133263 A133264 A133265 KEYWORD nonn AUTHOR Hao Zhang and Daniel Gildea (zhanghao(AT)cs.rochester.edu), Oct 15 2007 EXTENSIONS More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 10 2008 STATUS approved

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Last modified March 30 10:34 EDT 2023. Contains 361609 sequences. (Running on oeis4.)