Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #32 Apr 09 2023 02:27:04
%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
%C Also nonnegative numbers of the form 7*x^2 - 3*y^2. - _Jon E. Schoenfield_, Jun 03 2022
%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