A385880 Values of u in triples (u, v, w) such that the polynomial x^3 + u*x^2 + v*x + w has 3 distinct negative integer zeros; the triples are ordered by the inequality u < v.

6, 7, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16

Offset: 1

Author

Clark Kimberling, Jul 11 2025

Keywords

• nonn

Examples

			First 20 triples:
  u    v    w
  6   11    6
  7   14    8
  8   17   10
  8   19   12
  9   20   12
  9   23   15
  9   26   24
 10   23   14
 10   27   18
 10   29   20
 10   31   30
 11   26   16
 11   31   21
 11   34   24
 11   36   36
 11   38   40
 12   29   18
 12   35   24
 12   39   28
 12   41   30
		

Crossrefs

Cf. A385779, A386287, A386288.

Programs

Mathematica

z = 140;
t = Table[{b + c + d, c  d + d  b + b  c, b  c  d}, {b, 1, z - 2}, {c, b + 1, z - 1}, {d, c + 1, z}];
t1 = Union[Flatten[t, 2]];
t2 = Take[t1, 20]
Grid[t2]