OFFSET
0,3
COMMENTS
Discriminant = 28.
Also nonnegative integers of the form x^2 - 7y^2. - Colin Barker, Sep 29 2014
Also nonnegative integers of the form x^2 + bxy + cy^2 where b = -2n, c = n^2 - 7, for integer n. This includes both forms above: x^2 + 4xy - 3y^2 with n = -2 and x^2 - 7y^2 with n = 0. - Klaus Purath, Jan 14 2023
For the subsequence of numbers that are properly represented see A358946. - Wolfdieter Lang, Jan 18 2023
Proof for the proper equivalence of the above given family of forms F(n) = [1, -2*n, n^2 -7], for integer n, with the reduced principal form of discriminant 28, namely F_p = [1, 4, -3] given in the name: In matrix form MF(n) = Matrix([[1, -n], [-n, n^2 -7]]) = R(n)^T*MF_p(n)*R(n), with MF_p(n) = Matrix([[1, 2], [2, -3]]) and R(n) = Matrix([[1, -(n+2)], [0, 1]]) (T for transposed). - Wolfdieter Lang, Jan 20 2023
LINKS
R. J. Mathar, Table of n, a(n) for n = 0..1184
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)
MATHEMATICA
Reap[For[n = 0, n <= 300, n++, If[Reduce[x^2 + 4*x*y - 3*y^2 == n, {x, y}, Integers] =!= False, Sow[n]]]][[2, 1]]
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 31 2014
STATUS
approved