A387222 Number of noncongruent points in a face-centered cubic lattice that intersect a sphere of radius n centered on a point in the lattice.
1, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 4, 2, 5, 3, 7, 1, 6, 4, 6, 3, 8, 4, 7, 2, 11, 5, 9, 3, 9, 7, 9, 1, 11, 6, 17, 4, 11, 6, 13, 3, 12, 8, 12, 4, 18, 7, 13, 2, 17, 11, 16, 5, 15, 9, 21, 3, 17, 9, 16, 7, 17, 9, 22, 1, 29, 11, 18, 6, 20, 17, 19, 4, 20, 11, 30, 6, 26
Offset: 0
Examples
a(5) = 3: [5, 0, 0], [4, 3, 0], and [4, 1, 4*sqrt(1/2)], because this is the minimal set of points whose cuboctahedral rotations and reflections comprise all of the points in a fcc lattice that intersect a sphere of radius 5 centered on a point in the lattice.
Programs
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PARI
a(n)={if(!n, return(1)); my(c=0); for(x=0, n, for(y=0, min(x, sqrtint(n^2-x^2)), for(o=0, 1, my(m=2*(n^2-(x+o/2)^2-(y+o/2)^2)); if(!issquare(m), next); my(z=sqrtint(m)); if(z>=0 && z%2==o, c+=if(y+o && (x-y==z || x+y+o==z), 2, 1))))); c/3}
Comments