

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

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}] (* JeanFrançois Alcover, Feb 10 2016 *)


CROSSREFS

Cf. A000606.
Sequence in context: A290890 A152689 A217918 * 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



