

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
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OFFSET

0,2


REFERENCES

H. Gupta, A Table of Values of N_3(t), Proc. National Institute of Sciences of India, 13 (1947), 3563.
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}] (* JeanFrançois Alcover, Feb 10 2016 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



