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A243172 Nonnegative integers of the form x^2 + 3*x*y - 3*y^2 (discriminant 21). 4
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 (list; graph; refs; listen; history; text; internal format)
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

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 * A024797 A271253 A271542

Adjacent sequences:  A243169 A243170 A243171 * A243173 A243174 A243175

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 01 2014

STATUS

approved

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Last modified June 18 07:25 EDT 2021. Contains 345098 sequences. (Running on oeis4.)