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%I M1079 N0409 #22 Sep 24 2020 15:14:16
%S 0,0,1,2,4,7,14,24,43,82,149,284,534,1015,1937,3713,7136,13759,26597,
%T 51537,100045,194586,378987,739161,1443465,2821923,5522689,10818037,
%U 21208747,41612533,81704494,160531078,315602635,620831732,1221915127,2406177404,4740454046,9343415302,18423548106,36342329321
%N Number of integers <= 2^n of form 4 x^2 + 4 x y + 5 y^2.
%C Rewriting the expression as (2 x + y)^2 + 4 y^2 facilitates an efficient search without negative terms. - _Bert Dobbelaere_, Sep 24 2020
%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(4)=4 since 2^4=16 and 4=4*1^2, 5=5*1^2, 13=4*1^2+4*1*1+5*1^2, 16=4*2^2.
%o (PARI) a(n)=if(n<0,0,sum(k=1,2^n,0<sum(j=0,sqrtint(k)\2,issquare(k-4*j^2)&(k-j)%2==0)))
%K nonn
%O 0,4
%A _N. J. A. Sloane_
%E a(27)-a(39) from _Bert Dobbelaere_, Sep 24 2020