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

0, 16, 80, 516, 3794, 31456, 290970, 2974380, 33311520, 405773448, 5342413414, 75612301688

Offset: 3

Author

Isaac Lambert, Oct 07 2009

Keywords

• nonn

Comments

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.

Examples

			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).
		

Links

• W. M. Dymacek, I. Lambert, Permutations Avoiding Runs of i, i+1, i+2 or i, i-1, i-2 , J. Int. Seq. 14 (2011) # 11.1.6, Table 1.

Crossrefs

Cf. A095816, A165964, A078628.

Formula

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