cp's OEIS Frontend

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.

%I A072732 #5 May 01 2014 02:47:42
%S A072732 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,
%T A072732 25,9,10,30,59,97,112,72,41,19,22,48,83,127,144,98,61,33,14,15,38,70,
%U A072732 111,161,180,128,85,51,26,29,58,96,143,199,220,162,113,73,42,20,21,47
%N 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.
%H A072732 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o A072732 (Scheme) (define (A072732 n) (packA072732 (A025581 n) (A002262 n)))
%o A072732 (define (packA001477 x y) (/ (+ (expt (+ x y) 2) x (* 3 y)) 2))
%o A072732 (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)))))))
%Y A072732 Inverse: A072733, projections: A072736 & A072737, variant of the same theme: A072734. Cf. also A001477 and its projections A025581 & A002262.
%K A072732 nonn,tabl
%O A072732 0,3
%A A072732 _Antti Karttunen_, Jun 12 2002