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

1,1

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.

Links

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

Formula

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

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

Example

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}}.

Crossrefs

Cf. A005875, A016725.

Sequence in context: A371234 A371235 A152786 * A206039 A048069 A152787

Adjacent sequences: A267306 A267307 A267308 * A267310 A267311 A267312

Keyword

nonn

Author

Christopher Heiling, Jan 19 2016

Status

approved