A138801 Number of monomials in discriminant of symbolic principal (with two zeros coefficients by x^(n-1) and x^(n-2)) polynomial n degree.

1, 1, 2, 2, 6, 23, 92, 409, 1916, 9346, 47182, 244865, 1300086

Offset

1,3

Links

Table of n, a(n) for n=1..13.

Example

a(5)=6 because discriminant of quintic x^5+a*x^2+b*x+c is: -27*a^4*b^2 + 256*b^5 + 108*a^5*c - 1600*a*b^3*c + 2250*a^2*b*c^2 + 3125*c^4 that consists of 6 monomials (parts).

Mathematica

a = {1, 1}; Do[k = 0; Do[If[n > s - 3, If[(n > s - 1) && ((n > s - 2)), k = k + x^n], k = k + f[n] x^n], {n, 0, s}]; m = Resultant[k, D[k, x], x]; AppendTo[a, Length[m]], {s, 3, 9}]; a (* fixed by Vaclav Kotesovec, Mar 20 2019 *)
Flatten[{1, 1, Table[Length[Discriminant[x^n + Sum[Subscript[c, k]*x^k, {k, 0, n-3}], x]], {n, 3, 9}]}] (* Vaclav Kotesovec, Mar 20 2019 *)

Crossrefs

Cf. A007878, A138787, A138788, A138800, A138802.

Sequence in context: A184715 A292319 A290653 * A188958 A141902 A069466

Adjacent sequences: A138798 A138799 A138800 * A138802 A138803 A138804

Keyword

nonn,more

Author

Artur Jasinski, Mar 30 2008

Extensions

a(10)-a(12) from Vaclav Kotesovec, Mar 21 2019

a(13) from Vaclav Kotesovec, Mar 28 2019

Status

approved