OFFSET
0,2
LINKS
Colin Barker, Table of n, a(n) for n = 0..600
Wikipedia, Chebyshev polynomials.
Index entries for linear recurrences with constant coefficients, signature (36,-1).
FORMULA
a(0) = 1, a(1) = 18 and a(n) = 36*a(n-1) - a(n-2) for n > 1.
From Colin Barker, Dec 30 2018: (Start)
G.f.: (1 - 18*x) / (1 - 36*x + x^2).
a(n) = ((18+sqrt(323))^(-n) * (1+(18+sqrt(323))^(2*n))) / 2. (End)
E.g.f.: exp(18*x)*cosh(sqrt(323)*x). - Stefano Spezia, Aug 02 2025
MAPLE
seq(coeff(series((1-18*x)/(1-36*x+x^2), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Dec 31 2018
MATHEMATICA
Array[ChebyshevT[#, 18] &, 16, 0] (* or *)
With[{k = 18}, CoefficientList[Series[(1 - k x)/(1 - 2 k x + x^2), {x, 0, 15}], x]] (* Michael De Vlieger, Jan 01 2019 *)
PROG
(PARI) {a(n) = polchebyshev(n, 1, 18)}
(PARI) Vec((1 - 18*x) / (1 - 36*x + x^2) + O(x^20)) \\ Colin Barker, Dec 30 2018
(GAP) a:=[1, 18];; for n in [3..20] do a[n]:=36*a[n-1]-a[n-2]; od; Print(a); # Muniru A Asiru, Dec 31 2018
(Magma) I:=[1, 18]; [n le 2 select I[n] else 36*Self(n-1)-Self(n-2): n in [1..20]]; // Vincenzo Librandi, Jan 02 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Dec 29 2018
STATUS
approved