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A319617 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.

%I A319617 #7 Jan 30 2019 06:21:25
%S A319617 0,1,65,321,1257,2873,6265,11377,20161,31665,48945,71401,102041,
%T A319617 139481,188753,247329,323697,409457,516121,640393,789161,955793,
%U A319617 1153025,1376305,1637929,1921049,2252889,2615673,3033665,3483633,3990753,4547945,5173145,5840393,6589945,7395921,8287297,9238001,10281977,11402457,12633145,13929377
%N A319617 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 A319617 For n=2 there are 65 lattice points in Z^4 such that w^2+x^2+y^2+x^2 < 4
%o A319617 (Python)
%o A319617 for n in range (0,51):
%o A319617     NumPoints=0
%o A319617     for w in range (-n,n+1):
%o A319617         for x in range (-n,n+1):
%o A319617             for y in range (-n,n+1):
%o A319617                 for z in range (-n,n+1):
%o A319617                     if w**2+x**2+y**2+z**2<n**2:
%o A319617                         NumPoints+=1
%o A319617     print (n,NumPoints)
%Y A319617 a(n) = A055410(n) - A267326(n).
%K A319617 nonn,easy
%O A319617 0,3
%A A319617 _Brian J. Harrild_, Sep 24 2018