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A175375
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Number of integer triples (x,y,z) satisfying x^4+y^4+z^4=n, -n <= x,y,z <= n.
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2
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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, 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, 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
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: ( 1 + 2*Sum_{j>0} x^(j^4) )^3.
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EXAMPLE
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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.
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MAPLE
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N:= 200: # to get a(0)..a(N)
A:= Array(0..N):
for i from 0 while i^4 <= N do
if i=0 then ai:= 1 else ai:= 2 fi;
for j from 0 while i^4 + j^4 <= N do
if j=0 then aj:= 1 else aj:= 2 fi;
for k from 0 do
v:= i^4 + j^4 + k^4;
if v > N then break fi;
if k = 0 then ak:= 1 else ak:= 2 fi;
A[v]:= A[v] + ai*aj*ak;
od od od:
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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