A073201 Array of cycle count sequences for the table A073200.

1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 7, 4, 1, 1, 1, 22, 11, 3, 1, 1, 1, 66, 31, 7, 2, 1, 1, 1, 217, 96, 22, 4, 3, 1, 1, 1, 715, 305, 66, 11, 7, 2, 1, 1, 1, 2438, 1007, 217, 30, 22, 4, 2, 2, 1, 1, 8398, 3389, 715, 93, 66, 11, 3, 5, 1, 1, 1, 29414, 11636, 2438, 292, 217, 30, 6, 14, 2, 2, 1, 1

Offset

0,7

Comments

Each row of this table gives the counts of separate orbits/cycles to which the Catalan bijection given in the corresponding row of A073200 partitions each A000108(n) structures encoded in the range [A014137(n-1)..A014138(n-1)] of the sequence A014486/A063171.

Note that for involutions (self-inverse Catalan bijections) this is always (A000108(n)+Affffff(n))/2, where Affffff is the corresponding "fix-count sequence" from the table A073202.

Links

Table of n, a(n) for n=0..77.

A. Karttunen, Gatomorphisms (With the complete source and explanation)

Crossrefs

Only the first known occurrence(s) given (marked with ? if not yet proved/unclear): rows 0, 2, 4, etc.: A007595, Row 1: A073191, Rows 6 (& 8): A073431, Row 7: A000108, Rows 12, 14, 20, ...: A057513, Rows 16, 18, ...: A003239, Row 57, ..., 164: A007123, Row 168: A073193, Row 261: A002995, Row 2614: A057507, Row 2618 (?), row 17517: A001683.

Sequence in context: A132069 A259786 A254410 * A118654 A111760 A078424

Adjacent sequences: A073198 A073199 A073200 * A073202 A073203 A073204

Keyword

nonn,tabl

Author

Antti Karttunen, Jun 25 2002

Status

approved