A127285 Signature-permutation of a Catalan automorphism: SPINE-transformation of *A057508.

0, 1, 2, 3, 4, 6, 5, 7, 8, 9, 14, 10, 16, 19, 11, 15, 12, 17, 18, 13, 20, 21, 22, 23, 37, 25, 42, 51, 24, 38, 26, 44, 47, 27, 53, 56, 60, 28, 39, 29, 43, 52, 30, 40, 31, 45, 46, 32, 48, 49, 50, 33, 41, 34, 54, 55, 35, 57, 58, 59, 36, 61, 62, 63, 64, 65, 107, 70, 121, 149, 66

Offset

0,3

Comments

SPINE-transformation is explained in A122203. This automorphism permutes the top-level of a list of even length (1 ... 2n) as (2n 1 2n-1 2 2n-3 3 ... n+1 n) and when applied to a list of odd length (1 .. 2n+1), permutes it as (2n+1 1 2n 2 2n-1 3 ... n n+1). Used to construct A127287 and A127289.

Links

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

Index entries for signature-permutations of Catalan automorphisms

Prog

(Scheme) ;; Implementation of this automorphism, destructive, that acts on S-expressions, i.e. list-structures:
(define (*A127285! s) (cond ((pair? s) (*A057508! s) (*A127285! (cdr s)))) s)

Crossrefs

Inverse: A127286. a(n) = A127287(A057508(n)).

Sequence in context: A129606 A057510 A130920 * A130945 A073285 A057512

Adjacent sequences: A127282 A127283 A127284 * A127286 A127287 A127288

Keyword

nonn

Author

Antti Karttunen, Jan 16 2007

Status

approved