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A000604 Number of nonnegative solutions to x^2 + y^2 + z^2 <= n^2.
(Formerly M3419 N1383)
7
1, 4, 11, 29, 54, 99, 163, 239, 344, 486, 648, 847, 1069, 1355, 1680, 2046, 2446, 2911, 3443, 4022, 4662, 5395, 6145, 6998, 7913, 8913, 10006, 11194, 12437, 13751, 15216, 16710, 18361, 20123, 21950, 23919, 25956, 28150, 30415, 32876, 35385, 38049, 40876 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
REFERENCES
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).
LINKS
FORMULA
a(n) = [x^(n^2)] (1 + theta_3(x))^3/(8*(1 - x)), where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Apr 15 2018
MATHEMATICA
a[n_] := Sum[Boole[x^2 + y^2 + z^2 <= n^2], {x, 0, n}, {y, 0, Sqrt[n^2 - x^2]}, {z, 0, Sqrt[n^2 - x^2 - y^2]}]; A000604 = Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 100}] (* Jean-François Alcover, Feb 10 2016 *)
CROSSREFS
Column k=3 of A302998.
Cf. A000606.
Sequence in context: A152689 A217918 A360447 * A153876 A036881 A275012
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from David W. Wilson, May 22 2000
STATUS
approved

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Last modified June 12 11:18 EDT 2024. Contains 373331 sequences. (Running on oeis4.)