2nd try: Number of monomials in discriminant of a polynomial of degree n.

[Emeric Deutsch]

The Maple program

a:=proc(n) local p: p:=sum(A[i]*x^i,i=0..n): nops(discrim(p,x)) end: 
seq(a(n),n=1..8);

yields almost immediately

1, 2, 5, 16, 59, 246, 1103, 5247

I didn't have patience for a(9).

Emeric Deutsch



On Fri, 15 Dec 2006, N. J. A. Sloane wrote:

>
> I forgot that this microsoft mouse can only hold a few characters
> and truncates the rest
>
> Dear seqfans, at present i have this:
>
>
> %I A039744
> %S A039744 1,2,5,18,73,338,1656,8512,45207,246448
> %N A039744 Number of monomials in discriminant of a polynomial of degree n.
> %C A039744 Each monomial in the discriminant of a polynomial of degree n is an integer constant ti\
> mes the product of 2(n-1) of the coefficients,
> ed into the sum of 2(n-1) integers in the range 0..\
> n.
> %e A039744 Discriminant of cubic K3*x^3 + K2*x^2 + K1*x + K0 is -27*K3^2*K0^2 + 18*K3*K2*K1*K0 - 4\
> *K2^3*K0 - 4*K3*K1^3 + K2^2*K1^2 which contains 5 monomials.
> %Y A039744 Sequence in context: A073157 A045612 A103940 this_sequence A006848 A111916 A118187
> %Y A039744 Adjacent sequences: A039741 A039742 A039743 this_sequence A039745 A039746 A039747
> %K A039744 hard,nonn,nice
> %O A039744 1,2
> %A A039744 Bill Daly (bill.daly(AT)tradition.co.uk)
>
> A correspondent writes that
> %C A039744 This sequence is labelled "Number of monomials in discriminant of a polynomial of degree n." It is claimed that it starts as "1,2,5,18,73,...".
> I came upon this sequence in my own work and after repeated checks it seems to me that this sequence in fact starts as "1,2,5,16,59,...". Am I wrong?
>
> Could ssomeone check this?
>
> Neil
>