

A000592


Number of nonnegative solutions of x^2 + y^2 = z in first n shells.
(Formerly M2324 N0919)


2



1, 3, 4, 6, 8, 9, 11, 13, 15, 17, 19, 20, 22, 26, 28, 30, 31, 33, 35, 37, 39, 41, 43, 45, 48, 50, 52, 54, 56, 58, 62, 64, 65, 67, 69, 71, 73, 75, 79, 81, 83, 85, 86, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 112, 113, 117, 119, 121, 123, 127, 129, 131, 133, 135, 137
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OFFSET

0,2


COMMENTS

N_2(t) = Sum_{j <= t} n_2(j) where n_2(j) is the number of nonnegative solutions (x,y) of x^2 + y^2 = j, the solution (x,y) being considered as different from (y,x) in case x != y.


REFERENCES

Gupta, Hansraj; A table of values of N_2(t). Res. Bull. East Panjab Univ. 1952, (1952). no. 20, 1393.
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..2749


FORMULA

Cumulative totals of nonzero values in (or distinct values in cumulative totals of) A000925.  Franklin T. AdamsWatters, Jun 21 2006


MATHEMATICA

nn = 200; t = CoefficientList[Series[Sum[x^k^2, {k, 0, Sqrt[nn]}]^2, {x, 0, nn}], x]; Union[Accumulate[t]] (* JeanFrançois Alcover, Jul 20 2011, after T. D. Noe *)


CROSSREFS

Cf. A000925.
Sequence in context: A280762 A138097 A193732 * A138924 A188015 A192284
Adjacent sequences: A000589 A000590 A000591 * A000593 A000594 A000595


KEYWORD

nonn,nice,easy


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Franklin T. AdamsWatters, Jun 21 2006


STATUS

approved



