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

1,1

Links

Table of n, a(n) for n=1..70.

Example

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.

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]

Crossrefs

Cf. A385880, A386285, A386286.

Sequence in context: A092405 A130234 A108852 * A179413 A119476 A358700

Adjacent sequences: A385876 A385877 A385878 * A385880 A385881 A385882

Keyword

nonn

Author

Clark Kimberling, Jul 11 2025

Status

approved