A020542 a(n) = 5th Chebyshev polynomial (second kind) evaluated at 2^n.

6, 780, 30744, 1032240, 33423456, 1072693440, 34351350144, 1099444519680, 35183835219456, 1125895611878400, 36028762659231744, 1152921229728952320, 36893485948395872256, 1180591603125225308160, 37778931722219673452544, 1208925818488729268060160

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..663

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (42,-336,512).

Formula

From Colin Barker, May 03 2015: (Start)

a(n) = 2^(1+n)*(3-4^(2+n)+16^(1+n))

a(n) = 42*a(n-1)-336*a(n-2)+512*a(n-3) for n>2.

G.f.: -6*(88*x+1) / ((2*x-1)*(8*x-1)*(32*x-1)).

(End)

Maple

with(orthopoly):seq(U(5, 2^i), i=0..24);

Mathematica

Table[ChebyshevU[5, 2^n], {n, 1, 40}] (* Vladimir Joseph Stephan Orlovsky, Nov 03 2009 *)
LinearRecurrence[{42, -336, 512}, {6, 780, 30744}, 16] (* Jean-François Alcover, Dec 04 2017 *)

Prog

(PARI) Vec(-6*(88*x+1)/((2*x-1)*(8*x-1)*(32*x-1)) + O(x^100)) \\ Colin Barker, May 03 2015
(PARI) a(n) = polchebyshev(5, 2, 2^n) \\ Michel Marcus, May 03 2015

Crossrefs

Sequence in context: A088217 A242850 A364273 * A045480 A006114 A341554

Adjacent sequences: A020539 A020540 A020541 * A020543 A020544 A020545

Keyword

nonn,easy

Author

Simon Plouffe

Status

approved