A174076 Number of permutations of length n with no consecutive triples i,i+2,i+4 or i,i-2,i-4.

1, 1, 2, 6, 24, 108, 632, 4408, 35336, 319056, 3205824, 35451984, 427683560, 5588310904, 78615281768, 1184587864512, 19033796498496, 324852522308160, 5868833343451592, 111889157407344424

Offset: 0

Author

Isaac Lambert, Mar 10 2010

Keywords

• nonn
• more

Comments

Note for n<5 there are no such subsequences, so those values are trivially n!. Also note it is possible for a permutation to have both i,i+2,i+4 and i,i-2,i-4 triples, as in an example from n=7: (2,4,6,5,3,1,0). This permutation is not counted by a(7).

Examples

			For n=5 there are 5!-a(5)=12 permutations with i,i+2,i+4 or i,i-2,i-4 triples. An examples of one is (4,2,0,1,3).
		

Crossrefs

Cf. A095816, A174077, A174078, A174079.

Extensions

a(0)-a(4) and a(10)-a(19) from Alois P. Heinz, Apr 14 2021