A270050 Numbers of the form 2 * (x^2 + xy + y^2).

0, 2, 6, 8, 14, 18, 24, 26, 32, 38, 42, 50, 54, 56, 62, 72, 74, 78, 86, 96, 98, 104, 114, 122, 126, 128, 134, 146, 150, 152, 158, 162, 168, 182, 186, 194, 200, 206, 216, 218, 222, 224, 234, 242, 248, 254, 258, 266, 278, 288, 294, 296, 302, 312, 314, 326, 338, 342, 344

Offset

1,2

Comments

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.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

a(n) = 2 * A003136(n).

Example

6 is a term because 6 = (4^2 + 4*(-2) + (-2)^2) / 2.

Mathematica

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 *)

Prog

(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, ", ")));
(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

Crossrefs

Cf. A003136.

Sequence in context: A249624 A104636 A212014 * A137831 A117588 A174229

Adjacent sequences: A270047 A270048 A270049 * A270051 A270052 A270053

Keyword

nonn,easy

Author

Altug Alkan, Mar 09 2016

Status

approved