A020539 a(n) = 5th Chebyshev polynomial (first kind) evaluated at 2^n.

1, 362, 15124, 514088, 16695376, 536215712, 17174626624, 549713871488, 17591850501376, 562947269069312, 18014377034650624, 576460580504741888, 18446742699320037376, 590295799363589414912, 18889465843517650714624, 604462909103627145740288

Offset

0,2

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^n*(5-5*4^(1+n)+16^(1+n)).

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

G.f.: -(256*x^2+320*x+1) / ((2*x-1)*(8*x-1)*(32*x-1)).

(End)

Maple

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

Mathematica

Table[ChebyshevT[5, 2^n], {n, 1, 40}] (* Vladimir Joseph Stephan Orlovsky, Nov 03 2009 *)
LinearRecurrence[{42, -336, 512}, {1, 362, 15124}, 30] (* Harvey P. Dale, Jun 22 2019 *)

Prog

(PARI) Vec(-(256*x^2+320*x+1)/((2*x-1)*(8*x-1)*(32*x-1)) + O(x^100)) \\ Colin Barker, May 03 2015
(PARI) a(n) = polchebyshev(5, 1, 2^n) \\ Michel Marcus, May 03 2015

Crossrefs

Sequence in context: A031716 A243131 A155019 * A157442 A200558 A212324

Adjacent sequences: A020536 A020537 A020538 * A020540 A020541 A020542

Keyword

nonn,easy

Author

Simon Plouffe

Status

approved