A083928 Inverse function of N -> N injection A080298.

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0,40

Comments

a(1)=0 because A080298(0)=1, but a(n) = 0 also for those n which do not occur as values of A080298. All positive natural numbers occur here once.

For example, A057163 = A083928(A057163(A080298(n))), i.e. Catalan bijection A057163 embeds into itself in scale n:2n+1 using the obvious zigzag-tree -> binary tree embedding.

Links

Table of n, a(n) for n=0..98.

Antti Karttunen, Gatomorphisms

Prog

(Scheme-function showing the essential idea. For the full source, follow the "Catalan bijections" link.)
(define (ZigzagTree2BinTree_if_possible gt) (call-with-current-continuation (lambda (e) (let recurse ((gt gt)) (cond ((equal? gt '(() . ())) (list)) ((not (pair? gt)) (e '())) (else (cons (recurse (car gt)) (recurse (cdr gt)))))))))

Crossrefs

a(A080298(n)) = n for all n. Cf. A083925-A083927, A083929, A083935.

Sequence in context: A349436 A089811 A091888 * A074038 A204843 A204853

Adjacent sequences: A083925 A083926 A083927 * A083929 A083930 A083931

Keyword

nonn

Author

Antti Karttunen, May 13 2003

Status

approved