

A002102


Number of nonnegative solutions to x^2 + y^2 + z^2 = n.
(Formerly M2265 N0895)


6



1, 3, 3, 1, 3, 6, 3, 0, 3, 6, 6, 3, 1, 6, 6, 0, 3, 9, 6, 3, 6, 6, 3, 0, 3, 9, 12, 4, 0, 12, 6, 0, 3, 6, 9, 6, 6, 6, 9, 0, 6, 15, 6, 3, 3, 12, 6, 0, 1, 9, 15, 6, 6, 12, 12, 0, 6, 6, 6, 9, 0, 12, 12, 0, 3, 18, 12, 3, 9, 12, 6, 0, 6, 9, 18, 7, 3, 12, 6, 0, 6, 15, 9, 9, 6, 12, 15, 0, 3, 21, 18, 6, 0, 6
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OFFSET

0,2


REFERENCES

A. Das and A. C. Melissinos, Quantum Mechanics: A Modern Introduction, Gordon and Breach, 1986, p. 48.
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..10000


FORMULA

Coefficient of q^k in 1/8*(1 + theta_3(0, q))^3, or coefficient of q^n in (1+q+q^4+q^9+q^16+q^25+q^36+q^49+q^64+...)^3.


MATHEMATICA

a[n_] := Module[{x, y, z, c}, For[x=c=0, x^2<=n, x++, For[y=0, x^2+y^2<=n, y++, If[IntegerQ[Sqrt[nx^2y^2]], c++ ]]]; c]
CoefficientList[Series[Sum[q^n^2, {n, 0, 12}], {q, 0, 150}]^3, q]


PROG

(PARI) Vec(sum(k=0, 9, x^(k^2), O(x^100))^3) \\ Charles R Greathouse IV, Jun 13 2012


CROSSREFS

First differences of A000606.
Sequence in context: A002332 A302694 A245668 * A209334 A047655 A078685
Adjacent sequences: A002099 A002100 A002101 * A002103 A002104 A002105


KEYWORD

nonn


AUTHOR

N. J. A. Sloane.


EXTENSIONS

More terms from Dean Hickerson, Oct 07, 2001


STATUS

approved



