A072732 Simple triangle-stretching N X N -> N bijection: push terms in the middle twice as far down to make space for the terms obtained by bisecting the edges, which are thus contracted by the same factor. Do this for all "triangle-shells" successively contained inside each other in A001477.

0, 1, 4, 7, 12, 2, 3, 17, 24, 8, 11, 31, 40, 18, 5, 6, 23, 49, 60, 32, 13, 16, 39, 71, 84, 50, 25, 9, 10, 30, 59, 97, 112, 72, 41, 19, 22, 48, 83, 127, 144, 98, 61, 33, 14, 15, 38, 70, 111, 161, 180, 128, 85, 51, 26, 29, 58, 96, 143, 199, 220, 162, 113, 73, 42, 20, 21, 47

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: A072733, projections: A072736 & A072737, variant of the same theme: A072734. Cf. also A001477 and its projections A025581 & A002262.

Programs

Scheme

(define (A072732 n) (packA072732 (A025581 n) (A002262 n)))
(define (packA001477 x y) (/ (+ (expt (+ x y) 2) x (* 3 y)) 2))
(define (packA072732 x y) (let ((x-y (- x y))) (cond ((<= x-y 0) (packA001477 (+ (* 2 x) (modulo x-y 2)) (+ (* 2 x) (floor->exact (/ (1+ (- x-y)) 2))))) (else (packA001477 (+ (* 2 (1+ y)) (floor->exact (/ (- x-y 2) 2))) (+ (* 2 y) (modulo (1+ x-y) 2)))))))