A064640 Positions of non-crossing fixed-point-free involutions (encoded by A014486) in A055089, sorted to ascending order.

0, 1, 7, 23, 127, 143, 415, 659, 719, 5167, 5183, 5455, 5699, 5759, 16687, 16703, 26815, 28495, 36899, 36959, 38579, 40031, 40319, 368047, 368063, 368335, 368579, 368639, 379567, 379583, 389695, 391375, 399779, 399839, 401459, 402911, 403199

Offset

0,3

Comments

These permutations belong to the interpretation (kk) of the exercise 19 in the sixth chapter "Exercises on Catalan and Related Numbers" of Enumerative Combinatorics, Vol. 2, 1999 by R. P. Stanley, Wadsworth, Vol. 1, 1986: Fixed-point-free involutions w of [2n] such that if i < j < k < l and w(i) = k, then w(j) <> l.

From this, it follows that when they are subjected to the same automorphism as used in A061417 and A064636, one gets A002995.

Links

Table of n, a(n) for n=0..36.

R. P. Stanley, Exercises on Catalan and Related Numbers

Example

The first eight such permutations (after the identity) are in positions 1, 7, 23, 127, 143, 415, 659, 719 of A055089: 21, 2143, 4321, 214365, 432165, 216543, 632541, 654321 which written as disjoint cycles are (1 2), (1 2)(3 4), (1 4)(2 3), (1 2)(3 4)(5 6), (1 4)(2 3)(5 6), (1 2)(3 6)(4 5), (1 6)(2 3)(4 5), (1 6)(2 5)(3 4).

Maple

sort(A064638); or sort(A064639);

Crossrefs

For the needed Maple procedures see A064638. Cf. also A064639, A060112.

Sequence in context: A137367 A267926 A228698 * A064639 A064638 A082021

Adjacent sequences: A064637 A064638 A064639 * A064641 A064642 A064643

Keyword

nonn

Author

Antti Karttunen, Oct 02 2001

Status

approved