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%I M1095 N0417 #21 Oct 17 2017 03:59:37
%S 1,1,2,4,8,13,24,42,76,140,257,483,907,1717,3272,6261,12027,23172,
%T 44769,86708,168245,327073,636849,1241720,2424290,4738450,9271396,
%U 18157630,35591729,69820804,137069245,269270791,529312776,1041093937,2048826229,4034062310
%N Number of positive integers <= 2^n of form x^2 + 6 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)=4 since 2^3=8 and 1=1^2, 4=2^2, 6=6*1^2, 7=1^2+6*1^2.
%o (PARI) a(n)=if(n<0,0,sum(k=1,2^n,0<sum(y=0,sqrtint(k\6),issquare(k-6*y^2))))
%K nonn
%O 0,3
%A _N. J. A. Sloane_
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