A130918 Simple self-inverse permutation of natural numbers: List each block of A000108(n) numbers from A014137(n-1) to A014138(n-1) in reverse order.

0, 1, 3, 2, 8, 7, 6, 5, 4, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 196, 195, 194, 193, 192

Offset

0,3

Comments

In principle this involution is the signature permutation of yet another Catalan automorphism. However, the question remains what is the most "natural" way to create such an automorphism acting e.g. on S-expressions (i.e. rooted plane binary trees), which would produce this sequence as its signature permutation.

Links

A. Karttunen, Table of n, a(n) for n = 0..2055

A. Karttunen, Signature permutations of Catalan bijections

Index entries for signature-permutations of Catalan automorphisms

Formula

a(0)=0, a(n) = A014138(A072643(n)-1) - A082853(n).

Prog

(Scheme:) (define (A130918 n) (if (zero? n) n (- (A014138 (- (A072643 n) 1)) (A082853 n))))

Crossrefs

Inverse: A130918. Cf. A054429, A057163. The number of cycles and the number of fixed points in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A130380 and A036987.

Sequence in context: A082348 A122339 A057163 * A230432 A195305 A327575

Adjacent sequences: A130915 A130916 A130917 * A130919 A130920 A130921

Keyword

nonn

Author

Antti Karttunen, Jun 11 2007

Status

approved