A130374 -id:A130374 - cp's OEIS frontend

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

Offset: 0

Antti Karttunen, Jun 05 2007

nonn

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).

Antti Karttunen, Table of n, a(n) for n = 0..2055
Index entries for signature-permutations of Catalan automorphisms

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.

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

cp's OEIS Frontend

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.

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