A267309 Number of discrete vectors with integral components and integral length <= n in a 3-dimensional vectorspace (Partial sums of A016725).

6, 12, 42, 48, 78, 108, 162, 168, 270, 300, 378, 408, 486, 540, 690, 696, 798, 900, 1026, 1056, 1326, 1404, 1554, 1584, 1734, 1812, 2130, 2184, 2358, 2508, 2706, 2712, 3102, 3204, 3474, 3576, 3798, 3924, 4314, 4344, 4590, 4860, 5130, 5208, 5718

Offset: 1

Author

Christopher Heiling, Jan 19 2016

Keywords

• nonn

Comments

This sequence is Z_3(n), where Z_D(n) counts all vectors with integral components and length in a D-dimensional vectorpace within a certain radius. This sequence represents partial sums of A016725.

Examples

			For n = 2 the a(n)= 12 integral solutions of x^2 + y^2 + z^2 <= 2^2 are: {x,y,z} = {{0,0,1}; {0,1,0}; {1,0,0}; {0,0,-1}; {0,-1,0}; {-1,0,0}; {0,0,2}; {0,2,0}; {2,0,0}; {0,0,-2}; {0,-2,0}; {-2,0,0}}.
		

Links

• Christopher Heiling, Table of n, a(n) for n = 1..150

Crossrefs

Cf. A005875, A016725.

Formula

a(n) = Sum_{k=1..n} A005875(k^2).

a(n) = Sum_{k=1..n} A016725(k).