A085435 Resultant of the polynomial x^n-1 and the Chebyshev polynomial of the second kind U_2(x).

3, 9, 63, 225, 1023, 3969, 16383, 65025, 262143, 1046529, 4194303, 16769025, 67108863, 268402689, 1073741823, 4294836225, 17179869183, 68718952449, 274877906943, 1099509530625, 4398046511103, 17592177655809, 70368744177663, 281474943156225, 1125899906842623

Offset: 1

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 18 2003

Keywords

• nonn

Crossrefs

Cf. A085903.

Programs

PARI

a(n)={polresultant(x^n-1, polchebyshev(2, 2, x))} \\ Andrew Howroyd, Jul 10 2018

PARI

a(n)={4^n - 2^n - (-2)^n + (-1)^n} \\ Andrew Howroyd, Jul 10 2018

Formula

a(n) = 4^n - 2^n - (-2)^n + (-1)^n. Proof: Resultant(p, q) = (Leading Coefficient of q)^(Degree of p) * Product(p(i):i roots of q). - Luke Pebody, Oct 12 2004

Extensions

Terms a(11) and beyond from Andrew Howroyd, Jul 10 2018