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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 T. D. Noe, Table of n, a(n) for n=0..500 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 Adjacent sequences: A000601 A000602 A000603 * A000605 A000606 A000607 KEYWORD nonn AUTHOR N. J. A. Sloane 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.)