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A224212
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Number of nonnegative solutions to x^2 + y^2 <= n.
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10
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1, 3, 4, 4, 6, 8, 8, 8, 9, 11, 13, 13, 13, 15, 15, 15, 17, 19, 20, 20, 22, 22, 22, 22, 22, 26, 28, 28, 28, 30, 30, 30, 31, 31, 33, 33, 35, 37, 37, 37, 39, 41, 41, 41, 41, 43, 43, 43, 43, 45, 48, 48, 50, 52, 52, 52, 52, 52, 54, 54, 54, 56, 56, 56, 58, 62, 62, 62, 64
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 0..1000
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FORMULA
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G.f.: (1/(1 - x))*(Sum_{k>=0} x^(k^2))^2. - Ilya Gutkovskiy, Mar 14 2017
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MATHEMATICA
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nn = 68; t = Table[0, {nn}]; Do[d = x^2 + y^2; If[0 < d <= nn, t[[d]]++], {x, 0, nn}, {y, 0, nn}]; Accumulate[Join[{1}, t]] (* T. D. Noe, Apr 01 2013 *)
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PROG
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(Python)
for n in range(99):
k = 0
for x in range(99):
s = x*x
if s>n: break
for y in range(99):
sy = s + y*y
if sy>n: break
k+=1
print(str(k), end=', ')
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CROSSREFS
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Cf. A000925 (first differences).
Cf. A000606 (number of nonnegative solutions to x^2 + y^2 + z^2 <= n).
Cf. A057655 (number of integer solutions to x^2 + y^2 <= n).
Sequence in context: A100478 A112376 A161359 * A078490 A282847 A047877
Adjacent sequences: A224209 A224210 A224211 * A224213 A224214 A224215
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KEYWORD
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nonn
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AUTHOR
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Alex Ratushnyak, Apr 01 2013
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STATUS
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approved
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