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)).

1, 1, 1, 2, 2, 7, 26, 115, 521, 2502, 12389, 63236, 330455, 1762852

Offset

1,4

Links

Table of n, a(n) for n=1..14.

Example

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).

Mathematica

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 *)
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 *)

Crossrefs

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

Sequence in context: A342644 A069101 A221648 * A292016 A350020 A359582

Adjacent sequences: A138799 A138800 A138801 * A138803 A138804 A138805

Keyword

nonn,more

Author

Artur Jasinski, Mar 30 2008

Extensions

a(11)-a(13) from Vaclav Kotesovec, Mar 21 2019

a(14) from Vaclav Kotesovec, Mar 28 2019

Status

approved