A083927 Inverse function of N -> N injection A057123.

0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 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, 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, 4, 0, 0, 0, 0, 0, 0, 0, 5, 0

Offset

0,13

Comments

a(0)=0 because A057123(0)=0, but a(n) = 0 also for those n which do not occur as values of A057123. All positive natural numbers occur here once.

If g(n) = A083927(f(A057123(n))) then we can say that Catalan bijection g embeds into Catalan bijection f in scale n:2n, using the obvious binary tree -> general tree embedding. E.g. we have: A057163 = A083927(A057164(A057123(n))), A057117 = A083927(A072088(A057123(n))), A057118 = A083927(A072089(A057123(n))), A069770 = A083927(A072796(A057123(n))), A072797 = A083927(A072797(A057123(n))).

Links

Table of n, a(n) for n=0..100.

Antti Karttunen, Gatomorphisms

Prog

(Scheme-function showing the essential idea. For the full source, follow the "Catalan bijections" link.)
(define (Tree2BinTree_if_possible gt) (call-with-current-continuation (lambda (e) (let recurse ((gt gt)) (cond ((not (pair? gt)) gt) ((eq? 2 (length gt)) (cons (recurse (car gt)) (recurse (cadr gt)))) (else (e '())))))))

Crossrefs

a(A057123(n)) = n for all n. Cf. A083925-A083926, A083928-A083929, A083935.

Sequence in context: A173956 A306078 A284273 * A154724 A232747 A130460

Adjacent sequences: A083924 A083925 A083926 * A083928 A083929 A083930

Keyword

nonn

Author

Antti Karttunen, May 13 2003

Status

approved