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A267309 Number of discrete vectors with integral components and integral length <= n in a 3-dimensional vectorspace (Partial sums of A267651). 2
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 (list; graph; refs; listen; history; text; internal format)
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 A267651.

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} A267651(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, A267651.

Sequence in context: A052747 A007121 A152786 * A206039 A048069 A152787

Adjacent sequences:  A267306 A267307 A267308 * A267310 A267311 A267312

KEYWORD

nonn

AUTHOR

Christopher Heiling, Jan 19 2016

STATUS

approved

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Last modified October 15 15:03 EDT 2019. Contains 328030 sequences. (Running on oeis4.)