%I #16 May 10 2013 03:37:47
%S 1,1,1,2,3,3,4,4,5,5,6,6,7,8,8,9,9,10,11,11,12,12,13,13,14,15,15,16,
%T 16,17,17,18,19,19,20,20,21,21,22,23,23,24,24,25,25,26,27,27,28,28,29,
%U 30,30,31,31,32,32,33,34,34,35,35,36,36,37,38,38,39,39,40,41,41,42,42,43,43,44,45,45,46,46,47,47,48,49,49,50,50
%N Floor of the Euclidean distance of a point on the (1, 1, 1; 1, 1, 1) 3D walk.
%C Consider a standard 3-dimensional Euclidean lattice. We take 1 step along the positive x-axis, 1 along the positive y-axis, 1 along the positive z-axis, 1 along the positive x-axis, and so on. After 3, 6, 9, 12, 15 etc steps we have returned to the space diagonal (with equal x, y and z coordinates).
%C This sequence gives the floor of the Euclidean distance to the origin after n steps.
%F a(n) ~ n/sqrt(3). - _Charles R Greathouse IV_, May 02 2013
%F a(n) = floor(sqrt(A008810(n))), where A008810(n) is the squared Euclidean distance after n steps. - _R. J. Mathar_, May 02 2013
%o (JavaScript)
%o p = new Array(0, 0, 0);
%o for (a = 1; a < 100; a++) {
%o p[a%3] += 1;
%o document.write(Math.floor(Math.sqrt(p[0] * p[0] + p[1] * p[1] + p[2] * p[2])) + ", ");
%o }
%Y Cf. A213172, A224985.
%K nonn,easy
%O 1,4
%A _Jon Perry_, May 02 2013