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

Author

Antti Karttunen, Jun 11 2007

Keywords

• nonn

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

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.

Programs

Scheme

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

Formula

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