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, 28532970

Offset

1,3

Links

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

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

a(14) form Seiichi Manyama, Mar 26 2026

Status

approved