OFFSET
1,3
COMMENTS
Numbers represented by quadratic form with Gram matrix [ 1, 0, 0; 0, 1, 0; 0, 0, 2 ].
REFERENCES
L. E. Dickson, Integers represented by positive ternary quadratic forms, Bull. Amer. Math. Soc., 33 (1927) 63-70. [http://projecteuclid.org/euclid.bams/1183491956]
W. SierpiĆski, Elementary Theory of Numbers, (Ed. A. Schinzel) North-Holland 1988, see Exercise 4 on p. 395.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
G. Nebe and N. J. A. Sloane, Home page for this lattice
FORMULA
These are the numbers not of the form 4^k*(16*n + 14). [Dickson] - Everett W. Howe, May 18 2008
MAPLE
L := [seq(0, i=1..1)]: for x from 0 to 20 do for y from 0 to 20 do for z from 0 to 20 do if member(x^2+y^2+2*z^2, L)=false then L := [op(L), x^2+y^2+2*z^2] fi: od: od: od: L2 := sort(L): for i from 1 to 100 do printf(`%d, `, L2[i]) od:
MATHEMATICA
q=16; imax=q^2; Select[Union[Flatten[Table[x^2+y^2+2*z^2, {z, 0, q}, {y, 0, q}, {x, 0, q}]]], #<=imax&] (* Vladimir Joseph Stephan Orlovsky, Apr 19 2011 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from James A. Sellers, May 31 2000
STATUS
approved