A243193 Nonnegative integers represented by the indefinite quadratic form -3x^2+3xy+4y^2.

0, 1, 4, 6, 7, 9, 16, 19, 24, 25, 28, 36, 42, 43, 49, 54, 58, 61, 63, 64, 73, 76, 81, 82, 87, 96, 100, 106, 112, 114, 118, 121, 123, 133, 139, 142, 144, 150, 157, 159, 163, 168, 169, 171, 172, 175, 177, 178, 196, 199, 213, 214, 216, 225, 226, 229, 232, 244, 252

Offset: 1

Author

N. J. A. Sloane, Jun 06 2014

Keywords

• nonn

Comments

Discriminant 57.

Note that 4*y^2+3*x*y-3*x^2=n is equivalent to 19*y^2-3*z^2=4*n where z=2*x-y. - Robert Israel, Jun 09 2014

Links

• Robert Israel, Table of n, a(n) for n = 1..3030
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Primes: A141193.

Programs

Maple

select(m -> nops([isolve(-3*z^2+19*y^2=4*m)])>0, [$0..1000]); # Robert Israel, Jun 09 2014

Mathematica

Reap[For[n = 0, n <= 50, 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