This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
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).
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
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 *)
a(5)=6 because discriminant of quintic x^5+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).
a = {1, 1}; Do[k = 0; Do[If[n > s - 3, If[(n > s - 1) && ((n > s - 2)), 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, 9}]; 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-3}], x]], {n, 3, 9}]}] (* Vaclav Kotesovec, Mar 20 2019 *)
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).
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 *)