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Numbers represented by quadratic form with Gram matrix [ 4, 1; 1, 4 ] (divided by 2).
4

%I #17 Jul 12 2014 13:18:30

%S 0,2,3,5,8,12,17,18,20,23,27,30,32,38,45,47,48,50,53,57,62,68,72,75,

%T 80,83,92,93,95,98,102,107,108,113,120,122,125,128,137,138,147,152,

%U 153,155,158,162,167,170,173,180,183,188,192,197,200,207,212,218,227,228

%N Numbers represented by quadratic form with Gram matrix [ 4, 1; 1, 4 ] (divided by 2).

%C Numbers of the form 2*x^2 + x*y + 2*y^2, of discriminant -15. - _N. J. A. Sloane_, Jun 01 2014

%C 8*a(n) is of the form z^2 + 15*y^2, where z = 4*x + y. [_Bruno Berselli_, Jul 12 2014]

%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)

%F a(x, y) = (4x^2 + 2xy + 4y^2)/2; x, y any integer.

%e 32 is in the sequence because it can be written in the form 2*2^2+2*3+2*3^2, and hence 8*32 = 11^2+15*3^2.

%Y Cf. A028927. For primes see A106859.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_.

%E More terms from Larry Reeves (larryr(AT)acm.org), Mar 29 2000