A000592 Number of nonnegative solutions of x^2 + y^2 = z in first n shells.

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

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy

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

Crossrefs

Cf. A000925.

Programs

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 *)

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.

Extensions

More terms from Franklin T. Adams-Watters, Jun 21 2006