A322890 a(n) = value of Chebyshev T-polynomial T_n(20).

1, 20, 799, 31940, 1276801, 51040100, 2040327199, 81562047860, 3260441587201, 130336101440180, 5210183616019999, 208277008539359780, 8325870157958371201, 332826529309795488260, 13304735302233861159199, 531856585560044650879700

Offset: 0

Author

Seiichi Manyama, Dec 29 2018

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..624
• Wikipedia, Chebyshev polynomials.
• Index entries for sequences related to Chebyshev polynomials.
• Index entries for linear recurrences with constant coefficients, signature (40, -1).

Crossrefs

Column 20 of A322836.

Cf. A041758.

Programs

GAP

a:=[1,20];; for n in [3..20] do a[n]:=40*a[n-1]-a[n-2]; od; Print(a); # Muniru A Asiru, Dec 31 2018

Maple

seq(coeff(series((1-20*x)/(1-40*x+x^2),x,n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Dec 31 2018

Mathematica

CoefficientList[Series[(1 - 20 x)/(1 - 40 x + x^2), {x, 0, 15}], x] (* or *)
Array[ChebyshevT[#, 20] &, 16, 0] (* Michael De Vlieger, Jan 01 2019 *)

PARI

{a(n) = polchebyshev(n, 1, 20)}

PARI

Vec((1 - 20*x) / (1 - 40*x + x^2) + O(x^20)) \\ Colin Barker, Dec 30 2018

Formula

a(0) = 1, a(1) = 20 and a(n) = 40*a(n-1) - a(n-2) for n > 1.

From Colin Barker, Dec 30 2018: (Start)

G.f.: (1 - 20*x) / (1 - 40*x + x^2).

a(n) = ((20+sqrt(399))^(-n) * (1+(20+sqrt(399))^(2*n))) / 2.

(End)