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A080979
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Each tree encoded in A014486 mapped to the corresponding branch-reduced zigzag-tree (positions in A014486).
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4
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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; internal format)
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OFFSET
| 0,3
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COMMENTS
| For trees which are already branch-reduced we have a(n)=n, where n is one of A080980.
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REFERENCES
| R. Donaghey, Automorphisms on Catalan trees and bracketing, J. Combin. Theory, Series B, 29 (1980), 75-90.
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LINKS
| A. Karttunen, Gatomorphisms - with the complete Scheme source
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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)
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CROSSREFS
| Same sequence sorted, with duplicates removed: A080980. Cf. A080293.
Sequence in context: A175781 A072775 A090078 * A062789 A066069 A019530
Adjacent sequences: A080976 A080977 A080978 * A080980 A080981 A080982
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KEYWORD
| nonn
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AUTHOR
| Antti Karttunen (my_firstname.my_surname(AT)iki.fi) Mar 02 2003
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