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%I M1016 N0382 #18 Oct 17 2017 03:59:20
%S 1,2,4,6,10,18,33,60,111,205,385,725,1374,2610,4993,9578,18426,35568,
%T 68806,133411,259145,504222,982538,1917190,3745385,7324822,14339072,
%U 28095711,55095559,108124461,212342327,417283564,820520378,1614331755,3177789615,6258525127
%N Number of positive integers <= 2^n of form x^2 + 2 y^2.
%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 D. Shanks and L. P. Schmid, <a href="http://dx.doi.org/10.1090/S0025-5718-1966-0210678-1">Variations on a theorem of Landau. Part I</a>, Math. Comp., 20 (1966), 551-569.
%H <a href="/index/Qua#quadpop">Index entries for sequences related to populations of quadratic forms</a>
%e a(3)=6 since 2^3=8 and 1=1^2, 2=2*1^2, 3=1^2+2*1^2, 4=2^2, 6=2^2+2*1^2, 8=2*2^2.
%o (PARI) a(n)=if(n<0,0,sum(k=1,2^n,0<sum(y=0,sqrtint(k\2),issquare(k-2*y^2))))
%K nonn
%O 0,2
%A _N. J. A. Sloane_