cp's OEIS Frontend

A138802 Number of monomials in discriminant of symbolic Tschirnhausen polynomial of degree n (with three zero coefficients at x^(n-1), x^(n-2) and x^(n-3)).

%I A138802 #30 Mar 02 2023 04:32:45
%S A138802 1,1,1,2,2,7,26,115,521,2502,12389,63236,330455,1762852
%N A138802 Number of monomials in discriminant of symbolic Tschirnhausen polynomial of degree n (with three zero coefficients at x^(n-1), x^(n-2) and x^(n-3)).
%e A138802 a(5)=7 because discriminant of sextic x^6+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 A138802 a = {1, 1, 1}; Do[k = 0; Do[If[n > s - 4, If[(n > s - 1) && (n > s - 2) && (n > s - 3), 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, 4, 10}]; a (* _Artur Jasinski_, fixed by _Vaclav Kotesovec_, Mar 20 2019 *)
%t A138802 Flatten[{1, 1, 1, Table[Length[Discriminant[x^n + Sum[Subscript[c, k]*x^k, {k, 0, n-4}], x]], {n, 4, 10}]}] (* _Vaclav Kotesovec_, Mar 20 2019 *)
%Y A138802 Cf. A007878, A138787, A138788, A138800, A138801.
%K A138802 nonn,more
%O A138802 1,4
%A A138802 _Artur Jasinski_, Mar 30 2008
%E A138802 a(11)-a(13) from _Vaclav Kotesovec_, Mar 21 2019
%E A138802 a(14) from _Vaclav Kotesovec_, Mar 28 2019