A396333 - OEIS

%I #20 May 27 2026 19:26:21

%S 0,1,4,8,15,25,40,56,79,106,141,179,224,278,341,408,488,572,672,779,

%T 899,1028,1169,1324,1491,1669,1869,2077,2306,2539,2800,3064,3363,3668,

%U 3996,4341,4705,5090,5489,5916,6364,6825,7323,7834,8377,8937,9524,10127,10764

%N Number of ordered triples of integers (x,y,z) with 0 <= x <= y <= z and x^2 + y^2 + z^2 < n^2.

%H David A. Corneth, <a href="/A396333/b396333.txt">Table of n, a(n) for n = 0..4999</a>

%F The sequence a(n)/n^3 converges to Pi/36 as n->oo.

%e The integer triples (x,y,z) with 0 <= x <= y <= z and x^2 + y^2 + z^2 < 2^2 are exactly [0, 0, 0], [0, 0, 1], [0, 1, 1] and [1, 1, 1], so a(2) = 4.

%o (PARI) a(n) = sum(z=0,n,sum(y=0, z, sum(x=0, y, x^2+y^2+z^2 < n^2)))

%Y Cf. A000605, A078183, A117609, A255212, A394684.

%K nonn

%O 0,3

%A _Jean-Marc Rebert_, May 22 2026