|
%I #50 Mar 11 2023 06:26:58
%S 6,12,42,48,78,108,162,168,270,300,378,408,486,540,690,696,798,900,
%T 1026,1056,1326,1404,1554,1584,1734,1812,2130,2184,2358,2508,2706,
%U 2712,3102,3204,3474,3576,3798,3924,4314,4344,4590,4860,5130,5208,5718
%N Number of discrete vectors with integral components and integral length <= n in a 3-dimensional vectorspace (Partial sums of A016725).
%C 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.
%H Christopher Heiling, <a href="/A267309/b267309.txt">Table of n, a(n) for n = 1..150</a>
%F a(n) = Sum_{k=1..n} A005875(k^2).
%F a(n) = Sum_{k=1..n} A016725(k).
%e 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}}.
%Y Cf. A005875, A016725.
%K nonn
%O 1,1
%A _Christopher Heiling_, Jan 19 2016
|
