A123717 Signature permutation of a Catalan automorphism: row 253 of table A122203.

0, 1, 2, 3, 4, 6, 5, 8, 7, 9, 11, 14, 16, 19, 10, 15, 13, 21, 22, 12, 20, 17, 18, 23, 25, 28, 30, 33, 37, 39, 42, 44, 47, 51, 53, 56, 60, 24, 29, 38, 43, 52, 27, 41, 35, 58, 59, 36, 62, 63, 64, 26, 40, 34, 57, 61, 31, 54, 45, 46, 32, 55, 48, 49, 50, 65, 67, 70, 72, 75, 79, 81

Offset: 0

Author

Antti Karttunen, Oct 11 2006

Keywords

• nonn

Comments

This is the signature-permutation of Catalan automorphism which is derived from nonrecursive Catalan automorphism *A123503 with the recursion schema SPINE (defined in A122203).

The number of fixed points in range [A014137(n-1)..A014138(n-1)] of this permutation begins as 1,1,2,1,3,1,4,1,8,1,16,1,47,..., the LCM of cycle sizes as 1,1,1,2,12,12,120,120,840,840,5040,5040,55440,... (cf. A089423) and the cycle-count sequence seems to be A045629. (To be proved.)

References

• A. Karttunen, paper in preparation, draft available by e-mail.

Links

• Index entries for signature-permutations of Catalan automorphisms

Crossrefs

Inverse: A123718. a(n) = A057509(A089854(n)). Row 253 of A122203.