A072735 - OEIS

A072735

Simple triangle-stretching N X N -> N bijection: Inverse of A072734, variant of A072733.

0, 1, 2, 3, 5, 9, 10, 6, 14, 20, 21, 15, 4, 27, 35, 36, 28, 7, 8, 44, 54, 55, 45, 11, 13, 19, 65, 77, 78, 66, 22, 16, 26, 34, 90, 104, 105, 91, 37, 29, 12, 43, 53, 119, 135, 136, 120, 56, 46, 17, 18, 64, 76, 152, 170, 171, 153, 79, 67, 23, 25, 33, 89, 103, 189, 209, 210

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..66.

Index entries for sequences that are permutations of the natural numbers

PROG

(Scheme) (define (A072735 n) (packA072735 (A025581 n) (A002262 n)))

(define (packA001477 x y) (/ (+ (expt (+ x y) 2) x (* 3 y)) 2))

(define (packA072735 x y) (cond ((<= x y) (let ((half-x (floor->exact (/ x 2)))) (packA001477 half-x (+ half-x (* 2 (- y (* 2 half-x))) (modulo x 2) (if (and (eq? x y) (even? x)) 0 -1))))) (else (let ((half-y (floor->exact (/ y 2)))) (packA001477 (+ half-y (* 2 (- (-1+ x) (* 2 half-y))) (modulo y 2) (if (and (eq? x (1+ y)) (even? y)) 1 0)) half-y)))))

CROSSREFS

Inverse: A072734, projections: A072781 & A072782, variant of the same theme: A072733. Cf. also A001477 and its projections A025581 & A002262.

Sequence in context: A342456 A100674 A058314 * A127149 A047606 A226826

Adjacent sequences: A072732 A072733 A072734 * A072736 A072737 A072738

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, Jun 12 2002

STATUS

approved