A383857 Number of permutations of [n] such that precisely one rising or falling succession occurs, but without either n(n-1) or (n-1)n.

0, 0, 2, 8, 34, 196, 1366, 10928, 98330, 983036, 10811134, 129714184, 1686103522, 23603603540, 354033474374, 5664286296416, 96289603698346, 1733166940314028, 32929480177913230, 658578501071986616, 13829959293448920434, 304255691156335505924

Offset: 1

Author

Wolfdieter Lang, May 19 2025

Keywords

• nonn
• easy

Comments

See A086852 or 2*A000130 for the counting including the successions n(n-1) and (n-1)n. See also the k = 1 columns of the triangles A001100 and 2*A086856.

For the number of permutations of length n without rising or falling successions see A002464(n).

Examples

			a(3) = 2*1 from the permutations 213 and the reverted 312.
a(4) = 2*4 from 1324, 1423, 2314, 3124 and the reverted 4231, 3241, 4132, 4213.
a(5) = 2*17 from the permutations corresponding to A086852(5) = 2*20, without 13542, 24513, 25413, and the reverted 24531, 31542, 31452.
		

Crossrefs

Cf. A000130, A001100, A002464, A086852, A086856.

Formula

a(n) = A002464(n+1) - (n-1) * A002464(n).