A138800 Number of monomials in discriminant of polynomial x^n + a_{n-2} x^{n-2} + ... + a_0.

1, 1, 2, 6, 19, 76, 320, 1469, 7048, 35233, 181656, 960800, 5189579

Offset

1,3

Links

Table of n, a(n) for n=1..13.

Example

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

Maple

1, 1, seq(nops(expand(discrim(x^n + add(c[i]*x^i, i=0..n-2), x))), n=3..12); # Robert Israel, Aug 10 2015

Mathematica

ClearAll[f]; a = {1, 1}; Do[k = 0; Do[If[n > s - 2, If[n > s - 1, 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, 8}]; a (* fixed by Vaclav Kotesovec, Mar 20 2019 *)
Flatten[{1, 1, Table[Length[Discriminant[x^n + Sum[Subscript[c, k]*x^k, {k, 0, n-2}], x]], {n, 3, 8}]}] (* Vaclav Kotesovec, Mar 20 2019 *)

Crossrefs

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

Sequence in context: A378586 A268569 A181770 * A008989 A057240 A079564

Adjacent sequences: A138797 A138798 A138799 * A138801 A138802 A138803

Keyword

nonn,more

Author

Artur Jasinski, Mar 30 2008

Extensions

a(2) and Mathematica program corrected [previously had erroneous a(2)=2 because of Length syntax in Mathematica] by Alan Sokal and Andrea Sportiello (sokal(AT)nyu.edu), Jun 17 2010

a(9) to a(12) from Robert Israel, Aug 10 2015

a(13) from Vaclav Kotesovec, Mar 28 2019

Status

approved