%I #6 Jan 12 2024 07:47:48

%S 0,1,0,2,0,3,0,6,0,0,0,4,0,0,0,14,0,0,0,0,0,7,0,16,0,0,0,0,0,0,0,42,0,

%T 0,0,5,0,0,0,15,0,0,0,11,0,0,0,39,0,0,0,0,0,0,0,43,0,0,0,0,0,0,0,123,

%U 0,0,0,0,0,8,0,19,0,0,0,0,0,0,0,51,0,0,0,0,0,20,0,53,0,0,0,0,0,0,0,154,0,0,0,0,0,0,0,52,0,0,0,0,0,0,0,151,0,0,0,0,0,0,0,155

%N Inverse function of N -> N injection A082856.

%C a(n) = 0 for those n which do not occur as the values of A082856. All positive natural numbers occur here once.

%H Antti Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/ACO1.htm">Alternative Catalan Orderings</a> (with the complete Scheme source)

%F a(A082856(n)) = n for all n.

%o (Scheme-functions showing the essential idea. For the full source, follow the "Alternative Catalan Orderings" link.)

%o (define A082857 (compose-funs A080300 parenthesization->binexp decode-A082856-code))

%o (define (decode-A082856-code code) (call-with-current-continuation (lambda (exit) (let recurse ((code code)) (cond ((zero? code) (list)) ((even? code) (exit '())) (else (let ((even-bits (A059905 (floor->exact (/ code 2)))) (odd-bits (A059906 (floor->exact (/ code 2))))) (cons (recurse odd-bits) (recurse even-bits)))))))))

%Y Cf. A082856, A072634-A072637, A075173-A075174.

%K nonn

%O 0,4

%A _Antti Karttunen_, May 06 2003