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A130374 Signature permutation of a Catalan automorphism: flip the positions of even and odd-indexedf elements at the top-level of list, leaving the last element in place if the length (A057515(n)) is odd. 2
0, 1, 2, 3, 4, 6, 5, 7, 8, 9, 10, 14, 16, 19, 11, 15, 12, 17, 18, 13, 20, 21, 22, 23, 25, 24, 26, 27, 37, 38, 42, 44, 47, 51, 53, 56, 60, 28, 29, 39, 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, 66, 70, 72, 75, 67, 71 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This self-inverse automorphism permutes the top-level of a list of even length (1 2 3 4 ... 2n-1 2n) as (2 1 4 3 ... 2n 2n-1) and when applied to a list of odd length (1 2 3 4 ... 2n-1 2n 2n+1), permutes it as (2 1 4 3 ... 2n 2n-1 2n+1).

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 (*A130374! s) (cond ((pair? s) (*A072796! s) (if (pair? (cdr s)) (*A130374! (cddr s))))) s)

CROSSREFS

Cf. a(n) = A057508(A130373(A057508(n))) = A057164(A130373(A057164(n))) = A127285(A127288(n)) = A127287(A127286(n)). Also a(A085223(n)) = A130370(A122282(A130369(A085223(n)))) holds for all n>=0. The number of cycles and the number of fixed points in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A073193 and A073192.

Sequence in context: A320454 A320455 A072796 * A122363 A122364 A122300

Adjacent sequences:  A130371 A130372 A130373 * A130375 A130376 A130377

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 05 2007

STATUS

approved

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Last modified January 17 18:27 EST 2019. Contains 319250 sequences. (Running on oeis4.)