

A123717


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


4



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
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OFFSET

0,3


COMMENTS

This is the signaturepermutation 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(n1)..A014138(n1)] 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 cyclecount sequence seems to be A045629. (To be proved.)


REFERENCES

A. Karttunen, paper in preparation, draft available by email.


LINKS

Table of n, a(n) for n=0..71.
Index entries for signaturepermutations of Catalan automorphisms


PROG

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


CROSSREFS

Inverse: A123718. a(n) = A057509(A089854(n)). Row 253 of A122203.
Sequence in context: A104650 A083179 A123503 * A123718 A121878 A167905
Adjacent sequences: A123714 A123715 A123716 * A123718 A123719 A123720


KEYWORD

nonn


AUTHOR

Antti Karttunen, Oct 11 2006


STATUS

approved



