2,2

For number of monomials in discriminant of symbolic polynomial n degree with all non-zero coefficients see A007878

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

For number of monomials in discriminant of symbolic Tschirnhausen (with three zeros coefficients by x^(n-1) and x^(n-2) and x^(n-3)) polynomial n degree see A138801

a(4)=6 because discriminant of quartic x^4+a*x^2+b*x+c is equal: -4a^3 b^2 - 27 b^4 + 16a^4 c + 144a b^2 c - 128 a^2 c^2 + 256c^3 consist of 6 monomials (parts)

ClearAll[f]; a = {1}; Do[k = 0; Do[If[n > s, If[n > s - 1, k = k + f[n] x^n], k = k + x^n], {n, 0, s}]; m = Resultant[k, D[k, x], x]; AppendTo[a, Length[m]], {s, 2, 8}]; a (*Artur Jasinski*)

Cf. A007878, A138787, A138788, A138801, A138802.

Sequence in context: A006250 A006249 A019575 this_sequence A103179 A004077 A007985

Adjacent sequences: A138797 A138798 A138799 this_sequence A138801 A138802 A138803

nonn

Artur Jasinski (grafix(AT)csl.pl), Mar 30 2008