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A020539 a(n) = 5th Chebyshev polynomial (first kind) evaluated at 2^n. 1

%I #25 Jun 22 2019 12:33:42

%S 1,362,15124,514088,16695376,536215712,17174626624,549713871488,

%T 17591850501376,562947269069312,18014377034650624,576460580504741888,

%U 18446742699320037376,590295799363589414912,18889465843517650714624,604462909103627145740288

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

%H Colin Barker, <a href="/A020539/b020539.txt">Table of n, a(n) for n = 0..663</a>

%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (42,-336,512).

%F From _Colin Barker_, May 03 2015: (Start)

%F a(n) = 2^n*(5-5*4^(1+n)+16^(1+n)).

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

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

%F (End)

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

%t Table[ChebyshevT[5,2^n],{n,1,40}] (* _Vladimir Joseph Stephan Orlovsky_, Nov 03 2009 *)

%t LinearRecurrence[{42,-336,512},{1,362,15124},30] (* _Harvey P. Dale_, Jun 22 2019 *)

%o (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

%o (PARI) a(n) = polchebyshev(5, 1, 2^n) \\ _Michel Marcus_, May 03 2015

%K nonn,easy

%O 0,2

%A _Simon Plouffe_

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)