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%I #11 May 01 2019 14:00:21
%S 1,6,12,8,0,0,0,0,0,0,0,0,0,0,0,0,6,24,24,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T 12,24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,24,24,0,0,0,0,0,0,0,0,0,0,0,0,0,24,48,0,0
%N Number of integer triples (x,y,z) satisfying x^4+y^4+z^4=n, -n <= x,y,z <= n.
%C 4th power variant of A004018 and A175361.
%H Robert Israel, <a href="/A175375/b175375.txt">Table of n, a(n) for n = 0..10000</a>
%F G.f.: ( 1 + 2*Sum_{j>0} x^(j^4) )^3.
%e a(0) = 1 counts (x,y,z) = (0,0,0). a(3) = 8 counts (x,y,z) = (-1,-1,-1), (-1,-1,1), (-1,1,-1), (-1,1,1), (1,-1,-1), (1,-1,1), (1,1,-1) and (1,1,1). a(17) = 24 counts triples where one of x, y and z is 0, one is +-1 and the third +-2.
%p N:= 200: # to get a(0)..a(N)
%p A:= Array(0..N):
%p for i from 0 while i^4 <= N do
%p if i=0 then ai:= 1 else ai:= 2 fi;
%p for j from 0 while i^4 + j^4 <= N do
%p if j=0 then aj:= 1 else aj:= 2 fi;
%p for k from 0 do
%p v:= i^4 + j^4 + k^4;
%p if v > N then break fi;
%p if k = 0 then ak:= 1 else ak:= 2 fi;
%p A[v]:= A[v] + ai*aj*ak;
%p od od od:
%p seq(A[i],i=0..N); # _Robert Israel_, May 01 2019
%Y Cf. A004018, A175361.
%K nonn,look
%O 0,2
%A _R. J. Mathar_, Apr 24 2010
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