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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 (list; graph; refs; listen; history; text; internal format)
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 A121878 A167905

Adjacent sequences:  A123714 A123715 A123716 * A123718 A123719 A123720

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 11 2006

STATUS

approved

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Last modified February 29 07:24 EST 2020. Contains 332355 sequences. (Running on oeis4.)