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A020539 a(n) = 5th Chebyshev polynomial (first kind) evaluated at 2^n. 1
1, 362, 15124, 514088, 16695376, 536215712, 17174626624, 549713871488, 17591850501376, 562947269069312, 18014377034650624, 576460580504741888, 18446742699320037376, 590295799363589414912, 18889465843517650714624, 604462909103627145740288 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 17 08:39 EST 2019. Contains 329217 sequences. (Running on oeis4.)