%I #7 Jan 30 2019 06:21:25
%S 0,1,65,321,1257,2873,6265,11377,20161,31665,48945,71401,102041,
%T 139481,188753,247329,323697,409457,516121,640393,789161,955793,
%U 1153025,1376305,1637929,1921049,2252889,2615673,3033665,3483633,3990753,4547945,5173145,5840393,6589945,7395921,8287297,9238001,10281977,11402457,12633145,13929377
%N Number of Integer solutions to w^2 + x^2 + y^2 + z^2 < n^2; number of lattice points inside a 4-sphere of radius n.
%e For n=2 there are 65 lattice points in Z^4 such that w^2+x^2+y^2+x^2 < 4
%o (Python)
%o for n in range (0,51):
%o NumPoints=0
%o for w in range (-n,n+1):
%o for x in range (-n,n+1):
%o for y in range (-n,n+1):
%o for z in range (-n,n+1):
%o if w**2+x**2+y**2+z**2<n**2:
%o NumPoints+=1
%o print (n,NumPoints)
%Y a(n) = A055410(n) - A267326(n).
%K nonn,easy
%O 0,3
%A _Brian J. Harrild_, Sep 24 2018