A080979 Each tree encoded in A014486 mapped to the corresponding branch-reduced zigzag-tree (positions in A014486).

0, 1, 2, 3, 2, 5, 6, 7, 3, 2, 5, 11, 12, 5, 6, 15, 16, 7, 18, 6, 20, 7, 3, 2, 5, 11, 12, 5, 11, 29, 30, 12, 32, 11, 34, 12, 5, 6, 15, 39, 40, 15, 16, 43, 16, 7, 18, 47, 48, 49, 18, 6, 15, 53, 20, 55, 16, 57, 7, 18, 6, 20, 20, 7, 3, 2, 5, 11, 12, 5, 11, 29, 30, 12, 32, 11, 34, 12, 5, 11, 29

Offset

0,3

Comments

For trees which are already branch-reduced we have a(n)=n, where n is one of A080980.

Links

Table of n, a(n) for n=0..80.

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

Antti Karttunen, Gatomorphisms - with the complete Scheme source.

Prog

(Scheme-function implementing this surjection on trees represented as S-expressions:) (define (BranchReducedZigzagTree! bt) (cond ((pair? bt) (cond ((and (pair? (car bt)) (not (null? (caar bt))) (null? (cdar bt))) (set-car! bt (caar bt)) (BranchReducedZigzagTree! bt)) ((and (pair? (cdr bt)) (not (null? (cddr bt))) (null? (cadr bt))) (set-cdr! bt (cddr bt)) (BranchReducedZigzagTree! bt)) (else (BranchReducedZigzagTree! (car bt)) (BranchReducedZigzagTree! (cdr bt)))))) bt)

Crossrefs

Same sequence sorted, with duplicates removed: A080980. Cf. A080293.

Sequence in context: A325126 A327937 A259445 * A287620 A304491 A277803

Adjacent sequences: A080976 A080977 A080978 * A080980 A080981 A080982

Keyword

nonn

Author

Antti Karttunen, Mar 02 2003

Status

approved