A322888 Chebyshev T-polynomials T_n(16).

1, 16, 511, 16336, 522241, 16695376, 533729791, 17062657936, 545471324161, 17438019715216, 557471159562751, 17821639086292816, 569734979601807361, 18213697708171542736, 582268591681887560191, 18614381236112230383376, 595077930963909484707841

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..600

Wikipedia, Chebyshev polynomials.

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (32, -1).

Formula

a(0) = 1, a(1) = 16 and a(n) = 32*a(n-1) - a(n-2) for n > 1.

From Colin Barker, Dec 30 2018: (Start)

G.f.: (1 - 16*x) / (1 - 32*x + x^2).

a(n) = ((16+sqrt(255))^(-n) * (1+(16+sqrt(255))^(2*n))) / 2.

(End)

Maple

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

Mathematica

Array[ChebyshevT[#, 16] &, 17, 0] (* or *)
With[{k = 16}, CoefficientList[Series[(1 - k x)/(1 - 2 k x + x^2), {x, 0, 16}], x]] (* Michael De Vlieger, Jan 01 2019 *)

Prog

(PARI) {a(n) = polchebyshev(n, 1, 16)}
(PARI) Vec((1 - 16*x) / (1 - 32*x + x^2) + O(x^20)) \\ Colin Barker, Dec 30 2018
(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
(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

Crossrefs

Column 16 of A322836.

Sequence in context: A183890 A250400 A214624 * A291852 A301845 A302269

Adjacent sequences: A322885 A322886 A322887 * A322889 A322890 A322891

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 29 2018

Status

approved