Search: id:A000067
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%I A000067 M1016 N0382
%S A000067 1,2,4,6,10,18,33,60,111,205,385,725,1374,2610,4993,9578,18426,35568,68806,
%T A000067 133411,259145,504222,982538,1917190,3745385,7324822,14339072,28095711,
               55095559,
%U A000067 108124461,212342327,417283564,820520378,1614331755,3177789615,6258525127
%N A000067 Number of positive integers <= 2^n of form x^2 + 2 y^2.
%D A000067 D. Shanks and L. P. Schmid, Variations on a theorem of Landau. Part I, 
               Math. Comp., 20 (1966), 551-569.
%D A000067 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000067 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000067 <a href="Sindx_Qua.html#quadpop">Index entries for sequences related 
               to populations of quadratic forms</a>
%e A000067 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 A000067 (PARI) a(n)=if(n<0,0,sum(k=1,2^n,0<sum(y=0,sqrtint(k\2),issquare(k-2*y^2))))
%Y A000067 Sequence in context: A098197 A102477 A018074 this_sequence A133140 A026680 
               A164141
%Y A000067 Adjacent sequences: A000064 A000065 A000066 this_sequence A000068 A000069 
               A000070
%K A000067 nonn
%O A000067 0,2
%A A000067 N. J. A. Sloane (njas(AT)research.att.com).

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