cp's OEIS Frontend

A085690 Number of intersections between a sphere inscribed in a cube and the n X n X n cubes resulting from a cubic lattice subdivision of the enclosing cube.

%I A085690 #26 Jan 31 2025 17:37:44
%S A085690 8,26,56,98,152,194,272,362,440,530,656,746,872,1034,1160,1298,1496,
%T A085690 1658,1856,1994,2240,2450,2624,2906,3128,3362,3656,3890,4208,4442,
%U A085690 4760,5090,5360,5714,6032,6362,6752,7106,7496,7826,8216,8618,9080,9458,9896
%N A085690 Number of intersections between a sphere inscribed in a cube and the n X n X n cubes resulting from a cubic lattice subdivision of the enclosing cube.
%C A085690 A concise description of the problem is given by Clive Tooth in the Seaman, Tooth link. Sequence terms up to n=10 were first given by Dave Seaman. Cubes having at least one vertex on the sphere and all other vertices either all inside or all outside the sphere are counted as 1/2. a(n) is asymptotic to (3/2)*Pi*n^2. (Clive Tooth) The terms a(2),...,a(6) are identical with A005897(n-1) (points on surface of cube with square grid on its faces).
%H A085690 Hugo Pfoertner, <a href="/A085690/b085690.txt">Table of n, a(n) for n = 2..1000</a>
%H A085690 Hugo Pfoertner, <a href="/A085690/a085690_1.f.txt">FORTRAN program to count intersections.</a>
%H A085690 Dave Seaman, Clive Tooth, <a href="http://groups.google.com/group/sci.math/browse_thread/thread/590055b59dc3d406/6bf957c1724061fb">Sphere/Cube Intersections.</a> Discussion in Newsgroup sci.math.
%e A085690 a(2)=8 because all 8 cubes resulting from a 2*2*2 subdivision of a cube are intersected by a sphere inscribed in the large cube.
%e A085690 a(4)=56: 8 central cubes of 4*4*4=64 not intersected.
%o A085690 (Fortran) ! See Links.
%o A085690 (C#) // See Links.
%Y A085690 Cf. A005897, A008574.
%K A085690 nonn
%O A085690 2,1
%A A085690 _Hugo Pfoertner_, Jul 17 2003
%E A085690 Corrected overflow in program and b-file by _Hugo Pfoertner_, Apr 09 2016