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 A165963 Number of permutations of length n without increasing or decreasing modular 3-sequences 5

%I

%S 0,16,80,516,3794,31456,290970,2974380,33311520,405773448,5342413414,

%T 75612301688

%N Number of permutations of length n without increasing or decreasing modular 3-sequences

%C Increasing modular 3-sequences are of the following form: i,i+1,i+2, where arithmetic is modulo n, while correspondingly decreasing modular 3-sequences are of the form i,i-1,i-2, where arithmetic is modulo n.

%H W. M. Dymacek, I. Lambert, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Dymacek/dymacek5.html">Permutations Avoiding Runs of i, i+1, i+2 or i, i-1, i-2 </a>, J. Int. Seq. 14 (2011) # 11.1.6, Table 1.

%F Let b(n) be the sequence A165964. Then this sequence a(n)=n(b(n)).

%e For n=4 there are a(4)=16 solutions, thus there are 4!-a(4)=8 permutations of length 4 with increasing or decreasing modular 3-sequences. These are the permutations (0,1,2,3), (0,3,2,1), (1,2,3,0), (1,0,3,2), (2,3,0,1), (2,1,0,3), (3,0,1,2), and (3,2,1,0).

%Y Cf. A095816, A165964, A078628.

%K nonn

%O 3,2

%A _Isaac Lambert_, Oct 07 2009

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Last modified August 16 20:45 EDT 2022. Contains 356169 sequences. (Running on oeis4.)