A392944 - OEIS

%I #6 Feb 01 2026 20:25:15

%S 6,26,70,140,232,356,516,728,948,1228,1514,1942,2304,2742,3210,3816,

%T 4348,5072,5668,6516,7294,8098,8880,10100,10998,12048,13212,14528,

%U 15556,17152,18344,19946,21344,22784,24262,26558,28008,29658,31424,33822,35454,37874

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

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

%e 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.

%e 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.

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

%K nonn

%O 1,1

%A _Lorenzo Sauras Altuzarra_, Jan 27 2026

%E More terms from _Sean A. Irvine_, Feb 01 2026