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

%I #19 Jun 10 2014 09:40:09

%S 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,

%T 96,100,106,112,114,118,121,123,133,139,142,144,150,157,159,163,168,

%U 169,171,172,175,177,178,196,199,213,214,216,225,226,229,232,244,252

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

%C Discriminant 57.

%C 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

%H Robert Israel, <a href="/A243193/b243193.txt">Table of n, a(n) for n = 1..3030</a>

%H N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)

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

%t 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]]

%Y Primes: A141193.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Jun 06 2014

%E More terms from _Colin Barker_, Jun 10 2014