A020538 - OEIS

%I #22 Jun 13 2015 00:48:54

%S 1,97,1921,32257,522241,8380417,134184961,2147352577,34359214081,

%T 549753716737,8796084633601,140737454800897,2251799679467521,

%U 36028796482093057,576460750155939841,9223372028264841217,147573952555316674561,2361183241297383653377

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

%H Colin Barker, <a href="/A020538/b020538.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 From _Colin Barker_, May 03 2015: (Start)

%F   a(n) = (1-2^(3+2*n)+2^(3+4*n)).

%F   a(n) = 21*a(n-1)-84*a(n-2)+64*a(n-3) for n>2.

%F   G.f.: (32*x^2-76*x-1) / ((x-1)*(4*x-1)*(16*x-1)).

%F (End)

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

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

%o (PARI) Vec((32*x^2-76*x-1)/((x-1)*(4*x-1)*(16*x-1)) + O(x^100)) \\ _Colin Barker_, May 03 2015

%o (PARI) a(n) = polchebyshev(4, 1, 2^n) \\ _Michel Marcus_, May 03 2015

%K nonn,easy

%O 0,2

%A _Simon Plouffe_