A071652 Inverse permutation to A071651.

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, 126, 53, 21, 10, 40, 123, 149, 127, 154, 56, 18, 28, 38, 124, 151, 385, 155, 163, 47, 54, 30, 112, 122, 152, 387, 475, 164, 135, 156, 57, 13, 114, 376, 150, 388, 477, 503, 136

Offset

0,3

Links

Antti Karttunen, Rows n=0..66 of triangle, flattened

A. Karttunen, Alternative Catalan Orderings

Index entries for sequences that are permutations of the natural numbers

Prog

(Scheme functions below show the essential idea. For a complete source, see the "Alternative Catalan Orderings" OEIS Wiki page.)
(define arithrankA061579->lexrank (arithrank->lexrank-bijection A002262 A025581))
(define (arithrank->lexrank-bijection pr1 pr2) (lambda (n) (CatalanRankGlobal (parenthesization->binexp (unrank-bintree n pr1 pr2)))))
(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)))))
(define (A002262 n) (- n (binomial_n_2 (floor->exact (+ (/ 1 2) (sqrt (* 2 (1+ n))))))))
(define (A025581 n) (- (binomial_n_2 (1+ (floor->exact (+ (/ 1 2) (sqrt (* 2 (1+ n))))))) (1+ n)))

Crossrefs

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.

A071652(n) = A057163(A071654(n)). Cf. also A014486, A002262, A025581, A071653, A071654.

Sequence in context: A130264 A072659 A072766 * A089884 A172312 A086163

Adjacent sequences: A071649 A071650 A071651 * A071653 A071654 A071655

Keyword

nonn,tabl

Author

Antti Karttunen, May 30 2002

Status

approved