A385879 Values of u in triples (u, v, w) such that the polynomial x^3 + u*x^2 + v*x + w has 3 (possibly repeated) negative integer zeros; the triples are ordered by the inequality u < v.
3, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14
Offset: 1
Keywords
Examples
First 20 triples:
u v w
3 3 1
4 5 2
5 7 3
5 8 4
6 9 4
6 11 6
6 12 8
7 11 5
7 14 8
7 15 9
7 16 12
8 13 6
8 17 10
8 19 12
8 20 16
8 21 18
9 15 7
9 20 12
9 23 15
9 24 16
(x + 1)^3 = x^3 + 3*x^2 + 3*x + 1, so (3, 3, 1) is in the list; here the negative zeros are -1, -1, and -1.
Programs
-
Mathematica
z = 120; t = Table[{b + c + d, c d + d b + b c, b c d}, {b, 1, z}, {c, 1, z}, {d, 1, z}]; t1 = Union[Flatten[t, 2]]; t2 = Take[t1, 40] Grid[t2]