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

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

0,2

Comments

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.

Links

Table of n, a(n) for n=0..48.

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, ...

Formula

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

Crossrefs

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

Sequence in context: A144145 A075170 A039571 * A106455 A209445 A181427

Adjacent sequences: A080978 A080979 A080980 * A080982 A080983 A080984

Keyword

nonn

Author

Antti Karttunen, Mar 02 2003

Status

approved