A072734 Simple triangle-stretching N X N -> N bijection, variant of A072732.

0, 1, 2, 3, 12, 4, 7, 17, 18, 5, 6, 23, 40, 24, 8, 11, 31, 49, 50, 25, 9, 10, 30, 59, 84, 60, 32, 13, 16, 39, 71, 97, 98, 61, 33, 14, 15, 38, 70, 111, 144, 112, 72, 41, 19, 22, 48, 83, 127, 161, 162, 113, 73, 42, 20, 21, 47, 82, 126, 179, 220, 180, 128, 85, 51, 26, 29, 58

Offset: 0

Author

Antti Karttunen, Jun 12 2002

Keywords

• nonn
• tabl

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A072735, projections: A072740 & A072741, variant of the same theme: A072732. Used to construct the global arithmetic ranking scheme of plane binary trees presented in A072787/A072788. Cf. also A001477 and its projections A025581 & A002262.

Programs

Scheme

(define (A072734 n) (packA072734 (A025581 n) (A002262 n)))
(define (packA001477 x y) (/ (+ (expt (+ x y) 2) x (* 3 y)) 2))
(define (packA072734 x y) (let ((x-y (- x y))) (cond ((negative? x-y) (packA001477 (+ (* 2 x) (modulo (1+ x-y) 2)) (+ (* 2 x) (floor->exact (/ (+ (- x-y) (modulo x-y 2)) 2))))) ((< x-y 3) (packA001477 (+ (* 2 y) x-y) (* 2 y))) (else (packA001477 (+ (* 2 y) (floor->exact (/ (1+ x-y) 2)) (modulo (1+ x-y) 2)) (+ (* 2 y) (modulo x-y 2)))))))