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!)
A088317 a(n) = 8*a(n-1) + a(n-2), starting with a(0) = 1 and a(1) = 4. 4
1, 4, 33, 268, 2177, 17684, 143649, 1166876, 9478657, 76996132, 625447713, 5080577836, 41270070401, 335241141044, 2723199198753, 22120834731068, 179689877047297, 1459639851109444 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n+1)/a(n) converges to 4 + sqrt(17).

LINKS

Table of n, a(n) for n=0..17.

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (8,1).

FORMULA

a(n) = (((8+sqrt(68))/2)^n + ((8-sqrt(68))/2)^n)/2.

a(n) = A086594(n)/2.

E.g.f.: exp(4*x)*cosh(sqrt(17)*x); a(n) = ((4+sqrt(17))^n+(4-sqrt(17))^n)/2; a(n) = Sum_{k=0..floor(n/2)} C(n, 2*k)*17^k*4^(n-2*k). a(n) = T(n, 4*i)(-i)^n with T(n, x) Chebyshev's polynomials of the first kind (see A053120) and i^2=-1. - Paul Barry, Nov 15 2003

a(n) = A041024(n-1), n>0. [R. J. Mathar, Sep 11 2008]

G.f.: (1-4*x)/(1-8*x-x^2). [Philippe Deléham, Nov 16 2008]

a(n) = 1/2*((33+8*sqrt(17))*(4-sqrt(17))^(n+2)-(-33+8*sqrt(17))*(4+sqrt(17))^(n+2)). - Harvey P. Dale, May 07 2012

EXAMPLE

a(4) = 2177 = 8*a(3) + a(2) = 8*268 + 33 = (((8+sqrt(68))/2)^4 + ((8-sqrt(68))/2)^4)/2 = 2177.

MATHEMATICA

LinearRecurrence[{8, 1}, {1, 4}, 30] (* or *) With[{c=Sqrt[17]}, Simplify/@ Table[1/2 (c-4)((c+4)^n-(4-c)^n (33+8c)), {n, 30}]] (* Harvey P. Dale, May 07 2012 *)

PROG

(Maxima)

a[0]:1$ a[1]:4$ a[n]:=8*a[n-1]+a[n-2]$ A088317(n):=a[n]$

makelist(A088317(n), n, 0, 20); /* Martin Ettl, Nov 12 2012 */

CROSSREFS

Cf. A002018, A002190, A013192, A028576, A041027, A058153, A058155, A072754, A075132.

Cf. A041024.

Sequence in context: A081007 A213168 A203212 * A041024 A257068 A246806

Adjacent sequences:  A088314 A088315 A088316 * A088318 A088319 A088320

KEYWORD

nonn,easy

AUTHOR

Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Nov 06 2003

EXTENSIONS

Corrected generating function. - Philippe Deléham, Nov 20 2008

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 19:04 EDT 2018. Contains 315270 sequences. (Running on oeis4.)