A080970 -id:A080970 - 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.

A080971 A014486-encodings 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

42, 56, 170, 172, 184, 202, 212, 226, 232, 240, 682, 684, 690, 692, 696, 714, 724, 738, 744, 752, 810, 812, 824, 842, 850, 852, 856, 880, 906, 908, 916, 930, 936, 944, 962, 964, 968, 976, 992, 2730, 2732, 2738, 2740, 2744, 2762, 2764, 2770, 2772, 2776, 2786

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.
Antti Karttunen, Initial terms illustrated in positions 4, 8, 9, 10, 13, 14, 17, 19, 21, 22, 23, 24, 25, 26, 27, 28, 31, ...

Cf. A014486, A080970, A080981.

a(n) = A014486(A080970(n)).

A080980 A014486-indices 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, 1, 2, 3, 5, 6, 7, 11, 12, 15, 16, 18, 20, 29, 30, 32, 34, 39, 40, 43, 47, 48, 49, 53, 55, 57, 81, 82, 85, 89, 90, 91, 95, 97, 99, 113, 114, 116, 118, 123, 124, 136, 137, 139, 140, 141, 143, 146, 155, 159, 160, 161, 165, 167, 173, 183, 245, 246, 248, 250, 255, 256, 268

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.
R. P. Stanley, Exercises on Catalan and Related Numbers

Cf. A080979. a(n) = A080300(A080981(n)). See comment at A080981. Complement of A080970.

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

Original entry on oeis.org

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))

cp's OEIS Frontend

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

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A080971 A014486-encodings of the trees whose interior zigzag-tree (Stanley's c) is not branch-reduced (in the sense defined by Donaghey).

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A080980 A014486-indices of the trees whose interior zigzag-tree (Stanley's c) is branch-reduced (in the sense defined by Donaghey).

Views

Author

Keywords

Links

Crossrefs

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

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Author

Keywords

Comments

Crossrefs

Formula