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

 

Logo

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 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A048923 Indices of octagonal numbers which are also 9-gonal. 3
1, 459, 309141, 208360351, 140434567209, 94652689938291, 63795772583840701, 42998256068818693959, 28980760794611215887441, 19532989777311890689441051, 13165206129147419713467380709 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

As n increases, this sequence is approximately geometric with common ratio r = lim_{n->infinity} a(n)/a(n-1) = (sqrt(6) + sqrt(7))^4 = 337 + 52*sqrt(42). - Ant King, Jan 03 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Nonagonal Octagonal Number.

Index entries for linear recurrences with constant coefficients, signature (675,-675,1).

FORMULA

G.f.: x*(-1 + 216*x + 9*x^2) / ( (x-1)*(x^2 - 674*x + 1) ). - R. J. Mathar, Dec 21 2011

From Ant King, Jan 03 2012: (Start)

a(n) = 674*a(n-1) - a(n-2) - 224.

a(n) = (1/168)*((7*sqrt(6) + 2*sqrt(7))*(sqrt(6) + sqrt(7))^(4*n-3) + (7*sqrt(6) - 2*sqrt(7))*(sqrt(6) - sqrt(7))^(4*n-3) + 56).

a(n) = ceiling((1/168)*(7*sqrt(6) + 2*sqrt(7))*(sqrt(6) + sqrt(7))^(4*n-3)). (End)

MATHEMATICA

LinearRecurrence[{675, -675, 1}, {1, 459, 309141}, 30] (* Vincenzo Librandi, Dec 24 2011 *)

PROG

(Magma) I:=[1, 459, 309141]; [n le 3 select I[n] else 675*Self(n-1)-675*Self(n-2)+Self(n-3): n in [1..15]]; // Vincenzo Librandi, Dec 24 2011

CROSSREFS

Cf. A048922, A048924.

Sequence in context: A253527 A183964 A221816 * A329292 A252535 A264242

Adjacent sequences: A048920 A048921 A048922 * A048924 A048925 A048926

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 15:01 EST 2022. Contains 358667 sequences. (Running on oeis4.)