A071654 Inverse permutation to A071653.

0, 1, 3, 2, 8, 6, 5, 7, 19, 15, 4, 22, 16, 52, 14, 13, 20, 60, 43, 51, 41, 11, 18, 53, 178, 42, 153, 39, 10, 21, 47, 155, 177, 125, 151, 38, 12, 61, 56, 136, 154, 555, 123, 150, 40, 33, 55, 179, 164, 135, 479, 553, 122, 152, 117, 29, 17, 159, 557, 163, 417, 477, 552, 124

Offset

0,3

Comments

A014137(n-1) = A071654(A072638(n)) for n>0 - Antti Karttunen, Jul 30 2012, based on Paul D. Hanna's similar observation in A071653.

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 "Alternative Catalan Orderings" OEIS Wiki page.)
(define arithrankA001477->lexrank (arithrank->lexrank-bijection A025581 A002262))
(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: A071653. A071672 gives the corresponding parenthesizations (from the term 1 onward) encoded as binary numbers, i.e. A071672(n) = A063171(A071654(n)) for n >= 1.

a(n) = A057163(A071652(n)). Cf. also A014486, A002262, A025581, A071651, A071652.

Sequence in context: A132827 A126315 A125976 * A072657 A098163 A260323

Adjacent sequences: A071651 A071652 A071653 * A071655 A071656 A071657

Keyword

nonn,tabl

Author

Antti Karttunen, May 30 2002

Status

approved