A028955 Numbers represented by quadratic form with Gram matrix [ 4, 1; 1, 4 ] (divided by 2).

0, 2, 3, 5, 8, 12, 17, 18, 20, 23, 27, 30, 32, 38, 45, 47, 48, 50, 53, 57, 62, 68, 72, 75, 80, 83, 92, 93, 95, 98, 102, 107, 108, 113, 120, 122, 125, 128, 137, 138, 147, 152, 153, 155, 158, 162, 167, 170, 173, 180, 183, 188, 192, 197, 200, 207, 212, 218, 227, 228

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Numbers of the form 2*x^2 + x*y + 2*y^2, of discriminant -15. - N. J. A. Sloane, Jun 01 2014

8*a(n) is of the form z^2 + 15*y^2, where z = 4*x + y. [Bruno Berselli, Jul 12 2014]

Examples

			32 is in the sequence because it can be written in the form 2*2^2+2*3+2*3^2, and hence 8*32 = 11^2+15*3^2.
		

Links

• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Cf. A028927. For primes see A106859.

Formula

a(x, y) = (4x^2 + 2xy + 4y^2)/2; x, y any integer.

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Mar 29 2000