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 A020541 a(n) = 4th Chebyshev polynomial (second kind) evaluated at 2^n. 1

%I

%S 5,209,3905,64769,1045505,16764929,268386305,4294770689,68718690305,

%T 1099508482049,17592173461505,281474926379009,4503599426043905,

%U 72057593232621569,1152921501385621505,18446744060824649729,295147905127813218305,4722366482663486783489

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

%H Colin Barker, <a href="/A020541/b020541.txt">Table of n, a(n) for n = 0..829</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 (21,-84,64).

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

%F a(n) = 21*a(n-1) - 84*a(n-2) + 64*a(n-3) for n>2. - _Colin Barker_, May 03 2015

%F G.f.: (64*x^2-104*x-5) / ((x-1)*(4*x-1)*(16*x-1)). - _Colin Barker_, May 03 2015

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

%t Table[ChebyshevU[4,2^n],{n,1,40}] (* _Vladimir Joseph Stephan Orlovsky_, Nov 03 2009 *)

%o (PARI) Vec((64*x^2-104*x-5)/((x-1)*(4*x-1)*(16*x-1)) + O(x^100)) \\ _Colin Barker_, May 03 2015

%o (PARI) a(n) = polchebyshev(4, 2, 2^n) \\ _Michel Marcus_, May 03 2015

%K nonn,easy

%O 0,1

%A _Simon Plouffe_

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Last modified December 5 23:39 EST 2019. Contains 329784 sequences. (Running on oeis4.)