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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
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).
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
EXTENSIONS
More terms from David W. Wilson, May 22 2000
STATUS
approved