Lists of four numbers (a,b,c,d) such that a*x^2 + b*y^2 + c*z^2 + d*u^2 represents all nonnegative numbers, sorted.
1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 5, 1, 1, 1, 6, 1, 1, 1, 7, 1, 1, 2, 2, 1, 1, 2, 3, 1, 1, 2, 4, 1, 1, 2, 5, 1, 1, 2, 6, 1, 1, 2, 7, 1, 1, 2, 8, 1, 1, 2, 9, 1, 1, 2, 10, 1, 1, 2, 11, 1, 1, 2, 12, 1, 1, 2, 13, 1, 1, 2, 14, 1, 1, 3, 3, 1, 1, 3, 4
1
Like S000118, except sorted in Mathematica.
T. D. Noe, Plot of 54 * 4 terms
T. D. Noe, Table of 54 * 4 terms
(Mma) Monitor[nn = 10; mx = 20; t = {}; Do[u = Union[Flatten[Table[a*x^2 + b*y^2 + c*z^2 + d*u^2, {x, 0, nn}, {y, 0, nn}, {z, 0, nn}, {u, 0, nn}]]]; If[Complement[Range[nn^2], u] == {}, AppendTo[t, {a, b, c, d}]], {a, 1}, {b, mx}, {c, b, mx}, {d, c, mx}]; t, {a, b, c, d}]; Sort[t]
nonn,fini,full
T. D. Noe, Jul 08 2014