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Numbers represented by quadratic form with Gram matrix [ 2, 1; 1, 12 ] (divided by 2).
4

%I #14 Mar 28 2015 12:32:26

%S 0,1,4,6,8,9,12,16,18,23,24,25,26,27,32,36,39,48,49,52,54,58,59,62,64,

%T 72,78,81,82,87,92,93,94,96,100,101,104,108,116,117,121,123,124,128,

%U 138,141,142,144,146,150,156,162,164,167,169,173,174,184,186,188,192

%N Numbers represented by quadratic form with Gram matrix [ 2, 1; 1, 12 ] (divided by 2).

%C Nonnegative integers of the form x^2 + x*y + 6*y^2, discriminant -23. - _Ray Chandler_, Jul 12 2014

%C The Gram matrix is positive-definite, therefore, if w := (1 + sqrt(-23)) / 2, then |x + w*y|^2 = x^2 + x*y + 6*y^2 > 0 for all integers x and y except x = y = 0. - _Michael Somos_, Mar 28 2015

%C The theta function of the lattice with basis [1, w] is the g.f. of A028959, therefore, A028959(n) is positive if and only if n is in this sequence. - _Michael Somos_, Mar 28 2015

%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)

%Y For primes see A033217. Cf. A028929, A106867.

%Y Cf. A028959.

%K nonn

%O 1,3

%A _N. J. A. Sloane_.

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