This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A020540 #21 Jul 30 2015 17:02:14
%S A020540 4,56,496,4064,32704,262016,2096896,16776704,134216704,1073739776,
%T A020540 8589930496,68719468544,549755797504,4398046478336,35184372023296,
%U A020540 281474976579584,2251799813423104,18014398508957696,144115188074807296
%N A020540 a(n) = 8^(n+1) - 2^(n+2).
%C A020540 Third Chebyshev polynomial of second kind evaluated at 2^n.
%H A020540 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H A020540 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10, -16).
%F A020540 G.f.: 4(1+4x)/(1-10x+16x^2).
%F A020540 a(0)=4, a(1)=56, a(n) = 10*a(n-1) - 16*a(n-2). - _Harvey P. Dale_, Feb 27 2013
%e A020540 U_3(x) = 8x^3 - 4x so U_3(2^n) = 8(2^n)^3 - 4(2^n) = 8^(n+1) - 2^(n+2).
%p A020540 with(orthopoly):seq(U(3,2^i),i=0..24);
%t A020540 Table[ChebyshevU[3,2^n],{n,1,40}] (* _Vladimir Joseph Stephan Orlovsky_, Nov 03 2009 *)
%t A020540 Table[8^(n+1)-2^(n+2),{n,0,20}] (* or *) LinearRecurrence[{10,-16},{4,56},20] (* _Harvey P. Dale_, Feb 27 2013 *)
%o A020540 (PARI) a(n)=if(n<0,0,8^(n+1)-2^(n+2))
%K A020540 nonn
%O A020540 0,1
%A A020540 _Simon Plouffe_