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Signature permutation of a Catalan automorphism: flip the positions of even and odd-indiced elements at the top-level of list, leaving the first element in place if the length (A057515(n)) is odd.

+0
3

0, 1, 2, 3, 4, 6, 5, 7, 8, 9, 11, 10, 16, 19, 14, 15, 12, 17, 18, 13, 20, 21, 22, 23, 25, 24, 30, 33, 37, 29, 26, 44, 47, 27, 53, 56, 60, 28, 39, 38, 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, 67, 66, 72, 75, 79, 71 (list; graph; listen)

	OFFSET	`0,3`
	COMMENT	`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 5 ... 2n 2n+1), permutes it as (1 3 2 5 4 ... 2n+1 2n).`
	LINKS	`A. Karttunen, Table of n, a(n) for n = 0..2055` `Index entries for signature-permutations of Catalan automorphisms`
	CROSSREFS	`Cf. a(n) = A057508(A130374(A057508(n))) = A057164(A130374(A057164(n))). SPINE and ENIPS transform of *A130340 (transformations explained in A122203 and A122204). 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: A122364 A122300 A129608 this_sequence A121731 A129605 A057509` `Adjacent sequences: A130370 A130371 A130372 this_sequence A130374 A130375 A130376`
	KEYWORD	`nonn`
	AUTHOR	`Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Jun 05 2007`

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Last modified July 26 13:41 EDT 2008. Contains 142293 sequences.

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