A130339 Signature permutation of a Catalan automorphism: swap the two rightmost 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, 25, 24, 26, 27, 28, 29, 30, 44, 47, 33, 53, 56, 60, 37, 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, 72, 75, 70, 71

Offset

0,3

Comments

This self-inverse automorphism is obtained as either SPINE(*A129608) or ENIPS(*A129608). See the definitions given in A122203 and A122204.

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 (*A130339! s) (if (even? (length s)) (*A129608! s)) s)

Crossrefs

Cf. a(n) = A057508(A130340(A057508(n))) = A057164(A130340(A057164(n))). Row 3608 of A122285 and A122286. a(n) = A129608(n), if A057515(n) mod 2 = 0, otherwise a(n)=n.

Sequence in context: A275582 A129607 A130340 * A350348 A058812 A320454

Adjacent sequences: A130336 A130337 A130338 * A130340 A130341 A130342

Keyword

nonn

Author

Antti Karttunen, Jun 05 2007

Status

approved