A242663 Nonnegative integers of the form x^2 + 4*x*y - 4*y^2.

0, 1, 4, 8, 9, 16, 17, 25, 28, 32, 36, 41, 49, 56, 64, 68, 72, 73, 81, 89, 92, 97, 100, 112, 113, 121, 124, 128, 136, 137, 144, 153, 161, 164, 169, 184, 188, 193, 196, 200, 217, 224, 225, 233, 241, 248, 252, 256, 257, 272, 281, 284, 288, 289, 292

Offset: 1

Author

N. J. A. Sloane, May 31 2014

Keywords

• nonn

Comments

Discriminant 32.

Also numbers representable as x^2 + 6*x*y + y^2 with 0 <= x <= y. - Gheorghe Coserea, Jul 29 2018

Also numbers of the form x^2 - 8*y^2. - Jianing Song, Jul 31 2018

Links

• Gheorghe Coserea, Table of n, a(n) for n = 1..100001
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Cf. A031363.

Primes in this sequence = A007519.

Programs

Mathematica

Reap[For[n = 0, n <= 300, n++, If[Reduce[ x^2 + 4*x*y - 4*y^2 == n, {x, y}, Integers] =!= False, Sow[n]]]][[2, 1]]

PARI

seq(M, k=6) = {
setintersect([1..M], setbinop((x, y)->x^2 + k*x*y + y^2, [0..1+sqrtint(M)]));
};
concat(0, seq(292)) \\ Gheorghe Coserea, Jul 31 2018