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%I #22 Jul 05 2017 17:01:48
%S 0,2,6,8,14,18,24,26,32,38,42,50,54,56,62,72,74,78,86,96,98,104,114,
%T 122,126,128,134,146,150,152,158,162,168,182,186,194,200,206,216,218,
%U 222,224,234,242,248,254,258,266,278,288,294,296,302,312,314,326,338,342,344
%N Numbers of the form 2 * (x^2 + xy + y^2).
%C Integers of the form (x^2 + xy + y^2) / 2. See comments in A266836 about the numbers of the form x^2 + xy + y^2.
%H Charles R Greathouse IV, <a href="/A270050/b270050.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = 2 * A003136(n).
%e 6 is a term because 6 = (4^2 + 4*(-2) + (-2)^2) / 2.
%t Select[Range[0, 400], Resolve@ Exists[{x, y}, Reduce[# == (x^2 + x y + y^2)/2, {x, y}, Integers]] &] (* _Michael De Vlieger_, Mar 09 2016 *)
%o (PARI) x='x+O('x^700); p=eta(x)^3/eta(x^3); for(n=0, 699, if(polcoeff(p, n) != 0 && n % 2 == 0, print1(n/2, ", ")));
%o (PARI) list(lim)=my(v=List(), y, t); lim\=2; for(x=0, sqrtint(lim\3), my(y=x, t); while((t=x^2+x*y+y^2)<=lim, listput(v, 2*t); y++)); Set(v) \\ _Charles R Greathouse IV_, Jul 05 2017
%Y Cf. A003136.
%K nonn,easy
%O 1,2
%A _Altug Alkan_, Mar 09 2016
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