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%I #13 Apr 30 2014 01:53:47
%S 0,1,2,3,4,6,7,5,14,16,8,9,15,42,19,17,11,37,43,51,44,20,12,39,121,52,
%T 126,53,21,10,40,123,149,127,154,56,18,28,38,124,151,385,155,163,47,
%U 54,30,112,122,152,387,475,164,135,156,57,13,114,376,150,388,477,503,136
%N Inverse permutation to A071651.
%H Antti Karttunen, <a href="/A071652/b071652.txt">Rows n=0..66 of triangle, flattened</a>
%H A. Karttunen, <a href="https://oeis.org/wiki/Alternative_Catalan_Orderings">Alternative Catalan Orderings</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o (Scheme functions below show the essential idea. For a complete source, see the "Alternative Catalan Orderings" OEIS Wiki page.)
%o (define arithrankA061579->lexrank (arithrank->lexrank-bijection A002262 A025581))
%o (define (arithrank->lexrank-bijection pr1 pr2) (lambda (n) (CatalanRankGlobal (parenthesization->binexp (unrank-bintree n pr1 pr2)))))
%o (define (unrank-bintree rank pr1 pr2) (cond ((zero? rank) (list)) (else (cons (unrank-bintree (pr1 (-1+ rank)) pr1 pr2) (unrank-bintree (pr2 (-1+ rank)) pr1 pr2)))))
%o (define (A002262 n) (- n (binomial_n_2 (floor->exact (+ (/ 1 2) (sqrt (* 2 (1+ n))))))))
%o (define (A025581 n) (- (binomial_n_2 (1+ (floor->exact (+ (/ 1 2) (sqrt (* 2 (1+ n))))))) (1+ n)))
%Y Inverse permutation: A071651. A071671 gives the corresponding parenthesizations (from the term 1 onward) encoded as binary numbers, i.e. A071671(n) = A063171(A071652(n)) for n >= 1.
%Y A071652(n) = A057163(A071654(n)). Cf. also A014486, A002262, A025581, A071653, A071654.
%K nonn,tabl
%O 0,3
%A _Antti Karttunen_, May 30 2002
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