|
%I #22 Sep 08 2022 08:46:23
%S 1,16,511,16336,522241,16695376,533729791,17062657936,545471324161,
%T 17438019715216,557471159562751,17821639086292816,569734979601807361,
%U 18213697708171542736,582268591681887560191,18614381236112230383376,595077930963909484707841
%N Chebyshev T-polynomials T_n(16).
%H Colin Barker, <a href="/A322888/b322888.txt">Table of n, a(n) for n = 0..600</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev_polynomials">Chebyshev polynomials</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 (32, -1).
%F a(0) = 1, a(1) = 16 and a(n) = 32*a(n-1) - a(n-2) for n > 1.
%F From _Colin Barker_, Dec 30 2018: (Start)
%F G.f.: (1 - 16*x) / (1 - 32*x + x^2).
%F a(n) = ((16+sqrt(255))^(-n) * (1+(16+sqrt(255))^(2*n))) / 2.
%F (End)
%p seq(coeff(series((1-16*x)/(1-32*x+x^2),x,n+1), x, n), n = 0 .. 20); # _Muniru A Asiru_, Dec 31 2018
%t Array[ChebyshevT[#, 16] &, 17, 0] (* or *)
%t With[{k = 16}, CoefficientList[Series[(1 - k x)/(1 - 2 k x + x^2), {x, 0, 16}], x]] (* _Michael De Vlieger_, Jan 01 2019 *)
%o (PARI) {a(n) = polchebyshev(n, 1, 16)}
%o (PARI) Vec((1 - 16*x) / (1 - 32*x + x^2) + O(x^20)) \\ _Colin Barker_, Dec 30 2018
%o (GAP) a:=[1,16];; for n in [3..20] do a[n]:=32*a[n-1]-a[n-2]; od; Print(a); # _Muniru A Asiru_, Dec 31 2018
%o (Magma) I:=[1, 16]; [n le 2 select I[n] else 32*Self(n-1)-Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Jan 02 2019
%Y Column 16 of A322836.
%K nonn,easy
%O 0,2
%A _Seiichi Manyama_, Dec 29 2018
| 