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A000606
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Number of nonnegative solutions to x^2 + y^2 + z^2 <= n.
(Formerly M3294 N1329)
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13
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1, 4, 7, 8, 11, 17, 20, 20, 23, 29, 35, 38, 39, 45, 51, 51, 54, 63, 69, 72, 78, 84, 87, 87, 90, 99, 111, 115, 115, 127, 133, 133, 136, 142, 151, 157, 163, 169, 178, 178, 184, 199, 205, 208, 211, 223, 229, 229, 230, 239, 254, 260, 266, 278, 290, 290, 296
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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REFERENCES
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H. Gupta, A Table of Values of N_3(t), Proc. National Institute of Sciences of India, 13 (1947), 35-63.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, 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))^3. - Ilya Gutkovskiy, Mar 14 2017
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MATHEMATICA
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nn = 50; t = Table[0, {nn}]; Do[d = x^2 + y^2 + z^2; If[0 < d <= nn, t[[d]]++], {x, 0, nn}, {y, 0, nn}, {z, 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
for z in range(99):
sz = sy + z*z
if sz > n: break
k += 1
print(str(k), end=', ')
# Alex Ratushnyak, Apr 01 2013
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CROSSREFS
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Cf. A000604, A117609.
Cf. A002102 (first differences).
Sequence in context: A190765 A024621 A296029 * A215458 A061932 A270336
Adjacent sequences: A000603 A000604 A000605 * A000607 A000608 A000609
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Sean A. Irvine, Dec 01 2010
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STATUS
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approved
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