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%I #7 May 25 2015 03:58:31
%S 1,4,8,172,5204,222716,12509188,889421564,78097622276,8312906703868,
%T 1056520142488580,158263730949406716,27626236450406776836,
%U 5563092167972597137404,1280742543230231763615748,334405228960123174787678204,98317121153947856929753989124,32339023133437156084762282819580,11831483864832785151824395066146820,4789379698138059405310741712024371196
%N Number of two-dimensional simple permutations.
%C 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.
%H M. H. Albert, M. D. Atkinson and M. Klazar, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL6/Albert/albert.html">The enumeration of simple permutations</a>, Journal of Integer Sequences 6 (2003), Article 03.4.4.
%H Hao Zhang and Daniel Gildea, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL10/Zhang/dperm.html">Enumeration of Factorizable Multi-Dimensional Permutations</a>, J. Integer Sequences 10 (2007), Article 07.5.8.
%Y Cf. A006318, A111111.
%K nonn
%O 1,2
%A Hao Zhang and Daniel Gildea (zhanghao(AT)cs.rochester.edu), Oct 15 2007
%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 10 2008
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