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Number of solutions to n^2 < x^2 + y^2 + z^2 < (n+1)^2; number of lattice points between spheres of radii n and n+1.
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%I #4 Mar 30 2012 17:22:26

%S 0,20,60,128,228,380,440,684,860,1068,1328,1548,1940,2288,2484,2924,

%T 3300,3824,4140,4700,5240,5484,6260,6864,7340,8180,8676,9392,9804,

%U 10988,11208,12572,13100,13860,14792,15588,16604,17328,18500,19292

%N Number of solutions to n^2 < x^2 + y^2 + z^2 < (n+1)^2; number of lattice points between spheres of radii n and n+1.

%F a(n) = A078183(n+1) - A000605(n)

%t Table[Sum[SquaresR[3, k], {k, n^2 + 1, (n + 1)^2 - 1}], {n, 0, 50}]

%Y Cf. A000605, A078183.

%K nonn

%O 0,2

%A _T. D. Noe_, Nov 21 2002