A080971 -id:A080971 - cp's OEIS frontend

A080969 Orbit size of each non-branch-reduced tree encoded by A080971(n) under Donaghey's "Map M" Catalan automorphism.

2, 2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 3, 6, 6, 6, 6, 6, 2, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 20, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 20, 2, 6, 6, 6, 20, 20, 6, 6, 6, 6, 6, 20, 6, 6, 20, 6, 20, 6, 6, 20, 20, 6, 20, 6, 6, 6, 20, 20, 6, 6, 20, 20, 6, 20

Offset: 0

Antti Karttunen, Mar 02 2003

nonn

This is the size of the cycle containing A080970(n) in the permutations A057505/A057506.

Cf. A080968, A080972.

a(n) = A080967(A080970(n))

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

Original entry on oeis.org

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.

A080981 A014486-encodings of the trees whose interior zigzag-tree (Stanley's c) is branch-reduced (in the sense defined by Donaghey).

Original entry on oeis.org

0, 2, 10, 12, 44, 50, 52, 178, 180, 204, 210, 216, 228, 716, 722, 728, 740, 818, 820, 844, 866, 868, 872, 914, 920, 932, 2866, 2868, 2892, 2914, 2916, 2920, 2962, 2968, 2980, 3276, 3282, 3288, 3300, 3378, 3380, 3468, 3474, 3480, 3490, 3492, 3504, 3528, 3660

Offset: 0

Antti Karttunen, Mar 02 2003

nonn

Donaghey defines (on page 82 of his paper) the branch-reduced zigzag-trees as those zigzag-trees which do not contain longer than one-edge branches, where a branch is a maximal connected set of edges slanted to the same direction, with no perpendicular edges emanating from its middle. These form the primitive elements of the automorphism A057505/A057506.

Robert Donaghey, Automorphisms on Catalan trees and bracketing, J. Combin. Theory, Series B, 29 (1980), 75-90.
Antti Karttunen, Initial terms illustrated in positions 0, 1, 2, 3, 5, 6, 7, 11, 12, 15, 16, 18, 20, 29, 30, 32, ...

a(n) = A014486(A080980(n)). Cf. A080968, A080971. These trees are enumerated by A005554.

a(n) = A014486(A080980(n)).

A080970 A014486-indices of the trees whose interior zigzag-tree (Stanley's c) is not branch-reduced (in the sense defined by Donaghey).

Original entry on oeis.org

4, 8, 9, 10, 13, 14, 17, 19, 21, 22, 23, 24, 25, 26, 27, 28, 31, 33, 35, 36, 37, 38, 41, 42, 44, 45, 46, 50, 51, 52, 54, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 83, 84, 86, 87, 88, 92, 93, 94, 96, 98, 100, 101, 102, 103

Offset: 0

Antti Karttunen, Mar 02 2003

nonn

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

Cf. A014486, A080300, A080971.

See comment at A080971. Complement of A080980.

a(n) = A080300(A080971(n)).

cp's OEIS Frontend

A080969 Orbit size of each non-branch-reduced tree encoded by A080971(n) under Donaghey's "Map M" Catalan automorphism.

Views

Author

Keywords

Comments

Crossrefs

Formula

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

Views

Author

Keywords

Comments

Links

A080981 A014486-encodings of the trees whose interior zigzag-tree (Stanley's c) is branch-reduced (in the sense defined by Donaghey).

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

A080970 A014486-indices of the trees whose interior zigzag-tree (Stanley's c) is not branch-reduced (in the sense defined by Donaghey).

Views

Author

Keywords

Links

Crossrefs

Formula