1,4

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 polynomial n degree with only one zero coefficient by x^(n-1) see A138800

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

a(5)=7 because discriminant of sextic x^6+a*x^2+b*x+c is equal: -27a^4 b^2 + 256b^5 + 108a^5 c - 1600a b^3 c + 2250a^2 b c^2 + 3125 c^4 consist of 6 monomials (parts)

ClearAll[f]; a = {1, 1, 1}; Do[k = 0; Do[If[n > s, If[(n > s - 1) && (n > s - 2) && (n > s - 3), 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, 4, 10}]; a (*Artur Jasinski*)

Cf. A007878, A138787, A138788, A138800, A138801.

Sequence in context: A156464 A156520 A069101 this_sequence A047003 A067352 A062448

Adjacent sequences: A138799 A138800 A138801 this_sequence A138803 A138804 A138805

nonn

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