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A071652 Inverse permutation to A071651. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified October 21 07:08 EDT 2019. Contains 328292 sequences. (Running on oeis4.)