A000592 Number of nonnegative solutions of x^2 + y^2 = z in first n shells. (Formerly M2324 N0919)

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

Offset

0,2

Comments

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

References

Hansraj Gupta, A table of values of N_2(t), Res. Bull. East Panjab Univ. 1952, (1952). no. 20, 13-93.

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

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.

Mathematica

nn = 200; t = CoefficientList[Series[Sum[x^k^2, {k, 0, Sqrt[nn]}]^2, {x, 0, nn}], x]; Union[Accumulate[t]] (* Jean-François 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. Adams-Watters, Jun 21 2006

Status

approved