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

%I #33 Mar 02 2023 04:32:56

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

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

%e 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).

%t 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 *)

%t 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 *)

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

%K nonn,more

%O 1,3

%A _Artur Jasinski_, Mar 30 2008

%E a(10)-a(12) from _Vaclav Kotesovec_, Mar 21 2019

%E a(13) from _Vaclav Kotesovec_, Mar 28 2019