A130373 - OEIS

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A130373

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

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; 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 5 ... 2n 2n+1), permutes it as (1 3 2 5 4 ... 2n+1 2n).

LINKS

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

Index entries for signature-permutations of Catalan automorphisms

FORMULA

a(n) = A057508(A130374(A057508(n))) = A057164(A130374(A057164(n))).

CROSSREFS

Cf. A057508, A057164, A057164.

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 * A121731 A244322 A129605

Adjacent sequences: A130370 A130371 A130372 * A130374 A130375 A130376

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 05 2007

STATUS

approved