A216724 -id:A216724 - cp's OEIS frontend

A174073 Number of permutations of length n without modular consecutive triples i,i+2,i+4.

1, 1, 2, 3, 24, 100, 594, 4389, 35744, 325395, 3288600, 36489992, 441091944, 5770007009, 81213883898, 1223895060315, 19662509172096, 335472890422812, 6057979283966814, 115434096553014565, 2314691409661484600, 48723117262650147387, 1074208020519754180896, 24755214452825129257168

Offset: 0

Isaac Lambert, Mar 06 2010

nonn

			For example, a(5) does not count the permutation (0,4,1,3,2) since 4,1,3 is an arithmetic progression of 2 mod(5).

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

Max Alekseyev, Table of n, a(n) for n = 0..100
Kyle Parsons, Arithmetic Progressions in Permutations, thesis, 2011. See Table 4 p. 12.

Column k=0 of A216724.

Cf. A165960, A174072, A174074, A174075.

a(11)-a(17) from Alois P. Heinz, Apr 13 2021

Terms a(18) onward from Max Alekseyev, Feb 04 2024

A216726 Triangle read by rows: number of circular permutations of [1..n] with k modular progressions of rise 1, distance 2 and length 3 (n >= 3, 0 <= k <= n).

Original entry on oeis.org

11, 0, 0, 1, 6, 0, 0, 0, 0, 18, 5, 0, 0, 0, 1, 93, 18, 9, 0, 0, 0, 0, 600, 84, 28, 7, 0, 0, 0, 1, 4320, 512, 192, 0, 16, 0, 0, 0, 0, 35168, 4122, 810, 156, 54, 9, 0, 0, 0, 1, 321630, 34000, 5625, 1400, 200, 0, 25, 0, 0, 0, 0

Offset: 3

N. J. A. Sloane, Sep 15 2012

			Triangle begins:
1 0 0 1
6 0 0 0 0
18 5 0 0 0 1
93 18 9 0 0 0 0
600 84 28 7 0 0 0 1
4320 512 192 0 16 0 0 0 0
35168 4122 810 156 54 9 0 0 0 1
321630 34000 5625 1400 200 0 25 0 0 0 0
...

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

Cf. A216716, A216718, A216719, A216722, A216724, A174075.

cp's OEIS Frontend

A174073 Number of permutations of length n without modular consecutive triples i,i+2,i+4.

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