The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A322889 Chebyshev T-polynomials T_n(18). 2
 1, 18, 647, 23274, 837217, 30116538, 1083358151, 38970776898, 1401864610177, 50428155189474, 1814011722210887, 65253993844402458, 2347329766676277601, 84438617606501591178, 3037442904067381004807, 109263505928819214581874 (list; graph; refs; listen; history; text; internal format)
 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 (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) 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 Column 18 of A322836. Sequence in context: A350984 A281559 A166767 * A003298 A049869 A041615 Adjacent sequences: A322886 A322887 A322888 * A322890 A322891 A322892 KEYWORD nonn,easy AUTHOR Seiichi Manyama, Dec 29 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 2 12:48 EST 2023. Contains 367517 sequences. (Running on oeis4.)