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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A227139 Chebyshev S-polynomial evaluated at x = 48. 0

%I #11 Jun 13 2015 00:54:42

%S 1,48,2303,110496,5301505,254361744,12204062207,585540624192,

%T 28093745899009,1347914262528240,64671790855456511,

%U 3102898046799384288,148874434455514989313,7142869955817920102736,342708883444804649942015

%N Chebyshev S-polynomial evaluated at x = 48.

%C This sequence, with a(-1) = 0, appears in the solution of the Pell equation u^2 - 23*v^2 = +1 for the solutions v = 5*a(n), n >= -1, together with u = A114051(n+1).

%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 (48,-1).

%F a(n) = S(n, 48), with the Chebyshev S-polynomial, with coefficients given in A049310.

%F a(n) = 48*a(n-1) - a(n-2), n >= 1, a(-1) = 0, a(0) = 1.

%F O.g.f.: 1/(1 - 48*x + x^2).

%F a(n) = A174767(n+2)/5, n >= 0.

%t LinearRecurrence[{48,-1},{1,48},20] (* _Harvey P. Dale_, Aug 26 2013 *)

%Y Cf. A049310, A114051, A174767.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Jul 02 2013

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)