A130340 Signature permutation of a Catalan automorphism: swap the two leftmost subtrees of general trees, if the root degree (A057515(n)) is even.

0, 1, 2, 3, 4, 6, 5, 7, 8, 9, 10, 11, 16, 19, 14, 15, 12, 17, 18, 13, 20, 21, 22, 23, 24, 25, 26, 27, 37, 29, 30, 44, 47, 33, 53, 56, 60, 28, 38, 39, 43, 52, 42, 40, 31, 45, 46, 32, 48, 49, 50, 51, 41, 34, 54, 55, 35, 57, 58, 59, 36, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71

Offset

0,3

Comments

This is a self-inverse automorfism (an involution). Can be used to construct A130373.

Links

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

Index entries for signature-permutations of Catalan automorphisms

Prog

(Destructive Scheme implementation of this automorphism, which acts on S-expressions, i.e. list-structures:)
(define (*A130340! s) (if (even? (length s)) (*A072796! s)) s)

Crossrefs

Cf. a(n) = A057508(A130339(A057508(n))) = A057164(A130339(A057164(n))). a(n) = A072796(n), if A057515(n) mod 2 = 0, otherwise a(n)=n.

Sequence in context: A222245 A275582 A129607 * A130339 A350348 A058812

Adjacent sequences: A130337 A130338 A130339 * A130341 A130342 A130343

Keyword

nonn

Author

Antti Karttunen, Jun 05 2007

Status

approved