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

0,3

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

Table of n, a(n) for n=0..71.

Index entries for signature-permutations of Catalan automorphisms

Prog

(Scheme function, destructive implementation of this automorphism acting on S-expressions:) (define *A123717! (!SPINE *A123503!))

Crossrefs

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

Sequence in context: A104650 A083179 A123503 * A123718 A335430 A121878

Adjacent sequences: A123714 A123715 A123716 * A123718 A123719 A123720

Keyword

nonn

Author

Antti Karttunen, Oct 11 2006

Status

approved