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%I #23 Jun 13 2015 00:48:54
%S 1,26,244,2024,16336,130976,1048384,8388224,67108096,536869376,
%T 4294964224,34359732224,274877894656,2199023230976,17592185995264,
%U 140737488257024,1125899906646016,9007199254347776,72057594037141504,576460752301850624,4611686018424242176
%N a(n) = 4*8^n - 3*2^n.
%C 3rd Chebyshev polynomial (first kind) evaluated at powers of 2.
%H Colin Barker, <a href="/A020537/b020537.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-16).
%F a(n) = 10*a(n-1)-16*a(n-2). - _Colin Barker_, May 03 2015
%F G.f.: (16*x+1) / ((2*x-1)*(8*x-1)). - _Colin Barker_, May 03 2015
%p with(orthopoly):seq(T(3,2^i),i=0..24);
%t Table[ChebyshevT[3,2^n],{n,1,40}] (* _Vladimir Joseph Stephan Orlovsky_, Nov 03 2009 *)
%o (PARI) a(n) = polchebyshev(3, 1, 2^n); \\ _Michel Marcus_, Dec 28 2014
%o (PARI) Vec((16*x+1)/((2*x-1)*(8*x-1)) + O(x^100)) \\ _Colin Barker_, May 03 2015
%K nonn,easy
%O 0,2
%A _Simon Plouffe_