login
This site is supported by donations to The OEIS Foundation.

 

Logo

The October issue of the Notices of the Amer. Math. Soc. has an article about the OEIS.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A099368 Twice Chebyshev's polynomials of the first kind, T(n,x), evaluated at x=51/2. 4
2, 51, 2599, 132498, 6754799, 344362251, 17555720002, 894997357851, 45627309530399, 2326097788692498, 118585359913786999, 6045527257814444451, 308203304788622880002, 15712323016961952435651, 801020270560270951338199 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) and b(n):= A097836(n-1) with b(0) = 0 are the improper and proper nonnegative solutions of the Pell equation a(n)^2 - 53*(7*b(n))^2 = +4. - Wolfdieter Lang, Jun 27 2013

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..584

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (51, -1).

Index entries for sequences related to Chebyshev polynomials.

FORMULA

a(n)=51*a(n-1)-a(n-2), n >= 1; a(-1)=51, a(0)=2.

a(n) = S(n, 51) - S(n-2, 51) = 2*T(n, 51/2) with S(n, x) := U(n, x/2), S(-1, x) := 0, S(-2, x) := -1. S(n, 51)=A097836(n). U-, resp. T-, are Chebyshev's polynomials of the second, resp. first, case. See A049310 and A053120.

a(n)= ap^n + am^n, with ap:=(51 + 7*sqrt(53))/2 and am:=(51 - 7*sqrt(53))/2.

G.f.: (2-51*x)/(1-51*x+x^2).

MATHEMATICA

LinearRecurrence[{51, -1}, {2, 51}, 15] (* or *) CoefficientList[Series[(2 - 51 x)/(1 - 51 x + x^2), {x, 0, 14}], x] (* Michael De Vlieger, Feb 08 2017 *)

CROSSREFS

Sequence in context: A222850 A089304 A210907 * A132492 A030264 A129742

Adjacent sequences:  A099365 A099366 A099367 * A099369 A099370 A099371

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Oct 18 2004

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 22 18:50 EDT 2018. Contains 315270 sequences. (Running on oeis4.)