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A174074 Number of circular permutations of length n without consecutive triples i,i+2,i+4. 8

%I #14 Feb 04 2024 18:19:41

%S 1,1,1,2,6,22,109,657,4625,37186,336336,3379058,37328103,449669577,

%T 5866178493,82387080624,1239364493118,19881771085788,338797668091565,

%U 6111688544942463,116354993433563797,2331395107113471188,49042688584011866880,1080639600739277669092,24891049832682424745839

%N Number of circular permutations of length n without consecutive triples i,i+2,i+4.

%C Circular permutations are permutations whose indices are from the ring of integers modulo n.

%D Wayne M. Dymacek, Isaac Lambert and Kyle Parsons, Arithmetic Progressions in Permutations, http://math.ku.edu/~ilambert/CN.pdf, 2012.

%H Max Alekseyev, <a href="/A174074/b174074.txt">Table of n, a(n) for n = 0..100</a>

%H Kyle Parsons, <a href="http://hdl.handle.net/11021/23093">Arithmetic Progressions in Permutations</a>, thesis, 2011. See Table 3, p. 9.

%e Since a(5)=22, there are (5-1)!-22=2 circular permutations with consecutive triples i,i+2,i+4 in all circular permutations of length 5. They are exactly (0,2,4,1,3) and (0,2,4,3,1).

%Y Column 1 of A216719.

%Y Cf. A165961, A174072, A174073, A174075.

%K nonn

%O 0,4

%A _Isaac Lambert_, Mar 06 2010

%E a(10)-a(15) from _Donovan Johnson_, Sep 24 2010

%E a(0)-a(2) prepended and terms a(16) onward added by _Max Alekseyev_, Feb 04 2024

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)