A020541 a(n) = 4th Chebyshev polynomial (second kind) evaluated at 2^n.

5, 209, 3905, 64769, 1045505, 16764929, 268386305, 4294770689, 68718690305, 1099508482049, 17592173461505, 281474926379009, 4503599426043905, 72057593232621569, 1152921501385621505, 18446744060824649729, 295147905127813218305, 4722366482663486783489

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..829

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (21,-84,64).

Formula

a(n) = 16^(n+1) - 3*4^(n+1) + 1.

a(n) = 21*a(n-1) - 84*a(n-2) + 64*a(n-3) for n>2. - Colin Barker, May 03 2015

G.f.: (64*x^2-104*x-5) / ((x-1)*(4*x-1)*(16*x-1)). - Colin Barker, May 03 2015

Maple

with(orthopoly):seq(U(4, 2^i), i=0..24);

Mathematica

Table[ChebyshevU[4, 2^n], {n, 1, 40}] (* Vladimir Joseph Stephan Orlovsky, Nov 03 2009 *)

Prog

(PARI) Vec((64*x^2-104*x-5)/((x-1)*(4*x-1)*(16*x-1)) + O(x^100)) \\ Colin Barker, May 03 2015
(PARI) a(n) = polchebyshev(4, 2, 2^n) \\ Michel Marcus, May 03 2015

Crossrefs

Sequence in context: A292330 A068531 A144139 * A006413 A055316 A203470

Adjacent sequences: A020538 A020539 A020540 * A020542 A020543 A020544

Keyword

nonn,easy

Author

Simon Plouffe

Status

approved