A392944 a(n) is the number of cubic polynomials with coefficients in {-n, ..., n}, positive leading coefficient, and having three rational roots.

6, 26, 70, 140, 232, 356, 516, 728, 948, 1228, 1514, 1942, 2304, 2742, 3210, 3816, 4348, 5072, 5668, 6516, 7294, 8098, 8880, 10100, 10998, 12048, 13212, 14528, 15556, 17152, 18344, 19946, 21344, 22784, 24262, 26558, 28008, 29658, 31424, 33822, 35454, 37874

Offset

1,1

Comments

a(n) is also the number of cubic polynomials with coefficients in {-n, ..., n}, positive leading coefficient, and whose splitting field is Q.

Links

Table of n, a(n) for n=1..42.

Example

For n = 1, the a(1) = 6 polynomials with coefficients in {-1, 0, 1} are: x^3-x^2-x+1, x^3-x^2, x^3-x, x^3, x^3+x^2-x-1, x^3+x^2.
For n = 2, the a(2) = 26 polynomials with coefficients in {-2, -1, 0, 1, 2} are: x^3-2x^2-x+2, x^3-2x^2, x^3-2x^2+x, x^3-x^2-2x, x^3-x^2-x+1, x^3-x^2, x^3-x, x^3, x^3+x^2-2x, x^3+x^2-x-1, x^3+x^2, x^3+2x^2-x-2, x^3+2x^2, x^3+2x^2+x, 2x^3-2x^2-2x+2, 2x^3-2x^2, 2x^3-2x, 2x^3, 2x^3+2x^2-2x-2, 2x^3+2x^2, 2x^3-x^2-2x+1, 2x^3-x^2-x, 2x^3-x^2, 2x^3+x^2-2x-1, 2x^3+x^2-x, 2x^3+x^2.

Crossrefs

Cf. A391597 (quadratic, integer), A391527 (quadratic, rational), A391108 (cubic, integer).

Sequence in context: A190095 A135036 A166796 * A001701 A241452 A175898

Adjacent sequences: A392941 A392942 A392943 * A392945 A392946 A392947

Keyword

nonn

Author

Lorenzo Sauras Altuzarra, Jan 27 2026

Extensions

More terms from Sean A. Irvine, Feb 01 2026

Status

approved