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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..67.

Index entries for sequences that are permutations of the natural numbers

PROG

(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)))))))

CROSSREFS

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

Sequence in context: A128836 A061956 A178939 * A270684 A083487 A253129

Adjacent sequences:  A072729 A072730 A072731 * A072733 A072734 A072735

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, Jun 12 2002

STATUS

approved

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Last modified July 23 14:53 EDT 2017. Contains 289688 sequences.