A243192 Nonnegative integers represented by the indefinite quadratic form 3x^2+3xy-4y^2.

0, 2, 3, 8, 12, 14, 18, 21, 27, 29, 32, 38, 41, 48, 50, 53, 56, 57, 59, 71, 72, 75, 84, 86, 89, 98, 107, 108, 113, 116, 122, 126, 128, 129, 146, 147, 152, 162, 164, 167, 173, 174, 179, 183, 189, 192, 200, 203, 212, 219, 224, 227, 228, 236, 242, 243, 246, 257

Offset: 1

Author

N. J. A. Sloane, Jun 06 2014

Keywords

• nonn

Comments

Discriminant 57.

Note that 3*x^2+3*x*y-4*y^2=n is equivalent to 3*z^2 - 19*y^2=4*n where z=2*x+y. - Robert Israel, Jun 10 2014

Links

• Robert Israel, Table of n, a(n) for n = 1..3000
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Cf. A243193. Primes: A141192.

Programs

Maple

select(m -> nops([isolve(3*z^2-19*y^2=4*m)])>0, [$0..1000]); # Robert Israel, Jun 10 2014

Mathematica

Reap[For[n = 0, n <= 30, n++, If[Reduce[3*x^2 + 3*x*y - 4*y^2 == n, {x, y}, Integers] =!= False, Sow[n]]]][[2, 1]]

Extensions

More terms from Colin Barker, Jun 10 2014