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A080979 Each tree encoded in A014486 mapped to the corresponding branch-reduced zigzag-tree (positions in A014486). 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

REFERENCES

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

LINKS

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

A. 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: A243057 A090078 A259445 * A287620 A304491 A277803

Adjacent sequences:  A080976 A080977 A080978 * A080980 A080981 A080982

KEYWORD

nonn

AUTHOR

Antti Karttunen Mar 02 2003

STATUS

approved

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Last modified May 25 22:17 EDT 2019. Contains 323576 sequences. (Running on oeis4.)