A387062 a(n) = number of wiggly permutations |W_n|.

1, 1, 2, 5, 14, 51, 176, 807, 3232, 17449, 78384, 479897, 2366248, 16041147, 85534176, 631596455, 3602770400, 28633529345, 173300710720, 1469070416505, 9373542317760, 84152568224563, 563142033172480, 5323835899152567, 37206559614499840, 368667413713034441, 2681213937595142656

Offset: 0

Author

Michael De Vlieger, Aug 15 2025

Keywords

• nonn

Comments

Permutation P over [n] is said to be wiggly given the following two items hold for all pairs of values of the form (2*j-1, 2*j):

For upward order: if 2*j-1 appears before 2*j in P, then interposing terms are larger.

For downward order: if 2*j occurs before 2*j-1 in P, then interposing terms are smaller.

Examples

			W_2 = {12, 21},
W_3 = {123, 132, 213, 312, 321},
W_4 = {1234, 1243, 1342, 1423, 1432, 2134, 2143, 3412, 3421, 4123, 4132, 4213, 4312, 4321}.
		

Links

• Vincent Pilaud and Aaron Williams, Skipping Ropes: An Efficient Gray Code Algorithm for Generating Wiggly Permutations, Conf. Algor. Data Struct. Symp. (WADS 2025). See pp. 6-7.

Crossrefs

Cf. A344654.

Extensions

a(17)-a(26) from Alois P. Heinz, Aug 17 2025