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A243172 Nonnegative integers of the form x^2 + 3*x*y - 3*y^2 (discriminant 21). 4

%I

%S 0,1,4,7,9,15,16,25,28,36,37,43,49,51,60,63,64,67,79,81,85,100,105,

%T 109,112,121,123,127,135,141,144,148,151,163,169,172,175,177,193,196,

%U 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

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

%C Also numbers representable as x^2 + 5*x*y + y^2 with 0 <= x <= y. - _Gheorghe Coserea_, Jul 29 2018

%C 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

%H Gheorghe Coserea, <a href="/A243172/b243172.txt">Table of n, a(n) for n = 1..100001</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)

%t A={}; For[ n=0, n <= 300, n++,

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

%o (PARI)

%o \\ From Bill Allombert, Jun 04 2014. Since 21 is a fundamental discriminant, and the polynomial is unitary, the following code works:

%o B=bnfinit(x^2+3*x-3); select(n->#bnfisintnorm(B,n),[1..500])

%Y Cf. A031363.

%Y Primes: A141159.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Jun 01 2014

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Last modified July 28 00:54 EDT 2021. Contains 346316 sequences. (Running on oeis4.)