A243172 Nonnegative integers of the form x^2 + 3*x*y - 3*y^2 (discriminant 21).

0, 1, 4, 7, 9, 15, 16, 25, 28, 36, 37, 43, 49, 51, 60, 63, 64, 67, 79, 81, 85, 100, 105, 109, 112, 121, 123, 127, 135, 141, 144, 148, 151, 163, 169, 172, 175, 177, 193, 196, 204, 205, 211, 225, 235, 240, 249, 252, 256, 259, 267, 268, 277, 289, 295, 301, 303, 316, 324, 331, 333, 337, 340, 343, 357, 361, 373, 375, 379, 387, 393, 400, 415, 420, 421, 436, 441, 445, 448, 457, 459, 463, 469, 484, 487, 492, 499

Offset

1,3

Comments

Also numbers representable as x^2 + 5*x*y + y^2 with 0 <= x <= y. - Gheorghe Coserea, Jul 29 2018

Also numbers of the form x^2 - x*y - 5*y^2 with 0 <= x <= y (or x^2 + x*y - 5*y^2 with x, y nonnegative). - Jianing Song, Jul 31 2018

Also nonnegative numbers of the form 7*x^2 - 3*y^2. - Jon E. Schoenfield, Jun 03 2022

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)

Mathematica

A={}; For[ n=0, n <= 300, n++,
    If[ Length[ Reduce[x^2 + 3 x y - 3 y^2 - n == 0, {x, y}, Integers]]>0, AppendTo[A, n]]]; A

Prog

(PARI)
\\ From Bill Allombert, Jun 04 2014. Since 21 is a fundamental discriminant, and the polynomial is unitary, the following code works:
B=bnfinit(x^2+3*x-3); select(n->#bnfisintnorm(B, n), [1..500])

Crossrefs

Cf. A031363.

Primes: A141159.

Sequence in context: A010383 A010403 A032709 * A370523 A024797 A271253

Adjacent sequences: A243169 A243170 A243171 * A243173 A243174 A243175

Keyword

nonn

Author

N. J. A. Sloane, Jun 01 2014

Status

approved