A000592 - OEIS

%I M2324 N0919 #34 Sep 02 2023 04:37:22

%S 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,

%T 50,52,54,56,58,62,64,65,67,69,71,73,75,79,81,83,85,86,90,92,94,96,98,

%U 100,102,104,106,108,112,113,117,119,121,123,127,129,131,133,135,137

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

%C Cumulative totals of nonzero values in (or distinct values in cumulative totals of) A000925. - _Franklin T. Adams-Watters_, Jun 21 2006

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

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A000592/b000592.txt">Table of n, a(n) for n = 0..2749</a>

%F 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.

%t 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_ *)

%Y Cf. A000925.

%K nonn,nice,easy

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Franklin T. Adams-Watters_, Jun 21 2006