cp's OEIS Frontend

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

%I A242663 #31 Apr 23 2020 11:35:31
%S A242663 0,1,4,8,9,16,17,25,28,32,36,41,49,56,64,68,72,73,81,89,92,97,100,112,
%T A242663 113,121,124,128,136,137,144,153,161,164,169,184,188,193,196,200,217,
%U A242663 224,225,233,241,248,252,256,257,272,281,284,288,289,292
%N A242663 Nonnegative integers of the form x^2 + 4*x*y - 4*y^2.
%C A242663 Discriminant 32.
%C A242663 Also numbers representable as x^2 + 6*x*y + y^2 with 0 <= x <= y. - _Gheorghe Coserea_, Jul 29 2018
%C A242663 Also numbers of the form x^2 - 8*y^2. - _Jianing Song_, Jul 31 2018
%H A242663 Gheorghe Coserea, <a href="/A242663/b242663.txt">Table of n, a(n) for n = 1..100001</a>
%H A242663 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 A242663 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]]
%o A242663 (PARI)
%o A242663 seq(M, k=6) = {
%o A242663 setintersect([1..M], setbinop((x, y)->x^2 + k*x*y + y^2, [0..1+sqrtint(M)]));
%o A242663 };
%o A242663 concat(0, seq(292)) \\ _Gheorghe Coserea_, Jul 31 2018
%Y A242663 Cf. A031363.
%Y A242663 Primes in this sequence = A007519.
%K A242663 nonn
%O A242663 1,3
%A A242663 _N. J. A. Sloane_, May 31 2014