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A175362
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Number of integer pairs (x,y) satisfying |x|^3 + |y|^3 = n, -n <= x,y <= n.
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6
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1, 4, 4, 0, 0, 0, 0, 0, 4, 8, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 8, 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, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 8, 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, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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0,2
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COMMENTS
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Obviously, a(n) must be 4*k, for k >= 0, n > 0. - Altug Alkan, Apr 09 2016
a(k^3*n) >= a(n) for k >= 1.
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LINKS
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FORMULA
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G.f.: ( 1 + 2 * Sum_{j>=1} x^(j^3) )^2.
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EXAMPLE
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a(2) = 4 counts (x,y) = (-1,1), (1,1), (-1,-1) and (1,-1).
a(9) = 8 counts (x,y) = (-2,-1), (-2,1), (-1,-2), (-1,2), (1,-2), (1,2), (2,-1) and (2,1).
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MAPLE
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N:= 200: # to get a(0)..a(N)
G:= (1+2*add(x^(j^3), j=1..floor(N^(1/3))))^2:
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PROG
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(PARI) a(n) = if(n==0, 1, 4*sum(k=1, sqrtnint(n, 3), ispower(n - k^3, 3))); \\ Daniel Suteu, Aug 16 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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