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

1,2

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]

Links

Table of n, a(n) for n=1..60.

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

Formula

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

Example

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.

Crossrefs

Cf. A028927. For primes see A106859.

Sequence in context: A356235 A004170 A247116 * A246321 A104664 A338921

Adjacent sequences: A028952 A028953 A028954 * A028956 A028957 A028958

Keyword

nonn,easy

Author

N. J. A. Sloane.

Extensions

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

Status

approved