A080969 -id:A080969 - cp's OEIS frontend

A080972 a(n) = A080969(n)/A080967(A080979(A080970(n))).

1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 2, 1, 4, 1, 2, 1, 2, 2, 3, 3, 1, 2, 2, 1, 2, 4, 1, 1, 2, 1, 4, 4, 1, 2, 2, 1, 2, 4, 1, 2, 4, 2, 4, 1, 1, 4, 4, 1, 4, 1, 2, 1, 4, 4, 2, 1, 4, 4, 2, 4, 4, 2, 1

Offset: 0

Antti Karttunen, Mar 02 2003

nonn

Donaghey shows in his paper that the orbit size (under the automorphism A057505/A057506) of each non-branch-reduced tree encoded by A080971(n) is divisible by the orbit size of the corresponding branch-reduced tree. This sequence gives the corresponding ratio.

Robert Donaghey, Automorphisms on Catalan trees and bracketing, J. Combin. Theory, Series B, 29 (1980), 75-90.

A080967 Orbit size of each tree encoded by A014486(n) under Donaghey's "Map M" Catalan automorphism.

Original entry on oeis.org

1, 1, 2, 2, 2, 3, 3, 3, 2, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 6, 6, 6, 3, 6, 3, 2, 6, 3, 6, 5, 6, 6, 6, 6, 3, 5, 6, 6, 5, 6, 6, 6, 5, 5, 3, 6, 3, 6, 3, 6, 2, 6, 3, 3, 6, 6, 6, 6, 6, 2, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 20, 6, 6, 6, 6, 6, 24, 6, 6, 24, 6, 6, 6, 24, 24, 6, 6, 6, 6, 24, 20, 24, 2, 24, 6

Offset: 0

Antti Karttunen, Mar 02 2003

nonn

This is the size of the cycle containing n in the permutations A057505/A057506.

Cf. A080311, A080968, A080969, A080972.

A080968 Orbit size of each branch-reduced tree encoded by A080981(n) under Donaghey's "Map M" Catalan automorphism.

Original entry on oeis.org

1, 1, 2, 2, 3, 3, 3, 6, 6, 6, 6, 6, 6, 3, 2, 3, 5, 3, 5, 5, 5, 5, 3, 3, 2, 3, 6, 24, 24, 24, 24, 6, 24, 24, 24, 6, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 6, 24, 24, 24, 24, 24, 6, 24, 24, 6, 3, 18, 9, 24, 18, 18, 9, 18, 9, 18, 18, 3, 24, 15, 15, 24, 24, 18, 15, 15, 24, 3, 24, 24, 15, 15, 24

Offset: 0

Antti Karttunen, Mar 02 2003

nonn

This is the size of the cycle containing A080980(n) in the permutations A057505/A057506.

If the conjecture given in A080070 is true, then this sequence contains only six 2's. Questions: are there any (other) values with finite number of occurrences? Which primes will eventually appear?

Cf. A080969, A080972.

a(n) = A080967(A080980(n))

cp's OEIS Frontend

A080972 a(n) = A080969(n)/A080967(A080979(A080970(n))).

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A080967 Orbit size of each tree encoded by A014486(n) under Donaghey's "Map M" Catalan automorphism.

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A080968 Orbit size of each branch-reduced tree encoded by A080981(n) under Donaghey's "Map M" Catalan automorphism.

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