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A063725
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Number of ordered pairs (x,y) of positive integers such that x^2 + y^2 = n.
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10
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0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 2, 1, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 3, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 1, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 0, 2, 2, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| a(A018825(n))=0; a(A000404(n))>0; a(A081324(n))=1; a(A004431(n))>1. [Reinhard Zumkeller, Aug 16 2011]
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LINKS
| T. D. Noe, Table of n, a(n) for n = 0..10000
Index entries for sequences related to sums of squares
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FORMULA
| G.f.: (Sum_{m=1..inf} x^(m^2))^2.
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EXAMPLE
| a(5) = 2 from the solutions (1,2) and (2,1).
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MATHEMATICA
| nn = 100; t = Table[0, {nn}]; s = Sqrt[nn]; Do[n = x^2 + y^2; If[n <= nn, t[[n]]++], {x, s}, {y, s}]; Join[{0}, t] (* T. D. Noe, Apr 03 2011 *)
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PROG
| (Haskell)
a063725 n =
sum $ map (a010052 . (n -)) $ takeWhile (< n) $ tail a000290_list
a063725_list = map a063725 [0..]
-- Reinhard Zumkeller, Aug 16 2011
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CROSSREFS
| Cf. A000404 (the numbers n that can be represented in this form).
Cf. A000161, A063691, A063730.
Cf. A025426, A000290, A010052.
Sequence in context: A091979 A029430 A092303 * A084888 A091400 A129448
Adjacent sequences: A063722 A063723 A063724 * A063726 A063727 A063728
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Aug 23 2001
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