Search: id:A000072
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%I A000072 M1063 N0400
%S A000072 1,1,2,4,7,12,22,41,72,137,254,476,901,1716,3274,6286,12090,23331,45140,
%T A000072 87511,169972,330752,644499,1257523,2456736,4804666,9405749,18429828,36141339,
%U A000072 70928099,139295793,273741700,538277486,1059051586,2084763319,4105924366
%N A000072 Number of positive integers <= 2^n of form x^2 + 4 y^2.
%D A000072 D. Shanks and L. P. Schmid, Variations on a theorem of Landau. Part I, 
               Math. Comp., 20 (1966), 551-569.
%D A000072 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000072 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000072 <a href="Sindx_Qua.html#quadpop">Index entries for sequences related 
               to populations of quadratic forms</a>
%e A000072 a(3)=4 since 2^3=8 and 1=1^2, 4=2^2=4*1^2, 5=1^2+4*1^2, 8=2^2+1*1^2.
%o A000072 (PARI) a(n)=if(n<0,0,sum(k=1,2^n,0<sum(y=0,sqrtint(k\4),issquare(k-4*y^2))))
%Y A000072 Sequence in context: A026713 A002573 A064492 this_sequence A018179 A127542 
               A023432
%Y A000072 Adjacent sequences: A000069 A000070 A000071 this_sequence A000073 A000074 
               A000075
%K A000072 nonn
%O A000072 0,3
%A A000072 N. J. A. Sloane (njas(AT)research.att.com).

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