|
%I #20 Dec 07 2018 07:55:09
%S 1,1,72,186624,13604889600,24679069470425088,
%T 1036715783690392172494848,962459606796748852884396910313472,
%U 19112837387997044228759204010262201783812096,7926475921550134182551017087135940323782552453120000000,67406870957147550175650545441605700298239194363455522532832462241792
%N a(n) = 2^(n * (n - 1)/2) * 3^((n - 1) * (n - 2)) * n^(n - 3).
%C Discriminant of Fermat polynomials.
%C F(0)=0, F(1)=1 and F(n) = 3x F(n - 1) -2 F(n - 2) if n>1.
%H Muniru A Asiru, <a href="/A318184/b318184.txt">Table of n, a(n) for n = 1..39</a>
%H Rigoberto Flórez, Robinson Higuita, and Alexander Ramírez, <a href="https://arxiv.org/abs/1808.01264">The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials</a>, arXiv:1808.01264 [math.NT], 2018.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Discriminant.html">Discriminant</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FermatPolynomial.html">Fermat Polynomial</a>
%p seq(2^(n*(n-1)/2)*3^((n-1)*(n-2))*n^(n-3),n=1..12); # _Muniru A Asiru_, Dec 07 2018
%t F[0] = 0; F[1] = 1; F[n_] := F[n] = 3 x F[n - 1] - 2 F[n - 2];
%t a[n_] := Discriminant[F[n], x];
%t Array[a, 11] (* _Jean-François Alcover_, Dec 07 2018 *)
%o (PARI) a(n) = 2^(n*(n-1)/2) * 3^((n-1)*(n-2)) * n^(n-3); \\ _Michel Marcus_, Dec 07 2018
%Y Cf. A193678, A007701, A007701, A193678, A303941.
%K nonn
%O 1,3
%A _Rigoberto Florez_, Aug 20 2018
| 