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A071654 Inverse permutation to A071653. 8
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified October 18 15:18 EDT 2019. Contains 328161 sequences. (Running on oeis4.)