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

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A048924 9-gonal octagonal numbers. 3
1, 631125, 286703855361, 130242107189808901, 59165603001256545014625, 26877395137662573622784125461, 12209701798707362366915379264832801, 5546550074879110936730454426529871893125 (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))^8 = 227137+35048*sqrt(42).  - Ant King, Jan 03 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..100

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

Index to sequences with linear recurrences with constant coefficients, signature (454275,-454275,1).

FORMULA

a(n) = 454275*a(n-1) - 454275*a(n-2) + a(n-3). - Vincenzo Librandi, Dec 24 2011

Contribution from Ant King, Jan 03 2012: (Start)

G.f.: x*(1+176850*x+261*x^2) / ((1-x)*(1-454274*x+x^2)).

a(n) = 454274*a(n-1)-a(n-2)+177112.

a(n) = 1/672*((11*sqrt(7)-9*sqrt(6))*(sqrt(6)+sqrt(7))^(8n-5)-(11*sqrt(7)+9*sqrt(6))*(sqrt(6)-sqrt(7))^(8n-5)-262).

a(n) = floor(1/672*(11*sqrt(7)-9*sqrt(6))*(sqrt(6)+sqrt(7))^(8n-5)). (End)

MATHEMATICA

LinearRecurrence[{454275, -454275, 1}, {1, 631125, 286703855361}, 30] (* Vincenzo Librandi, Dec 24 2011 *)

PROG

(MAGMA) I:=[1, 631125, 286703855361]; [n le 3 select I[n] else 454275*Self(n-1)-454275*Self(n-2)+Self(n-3): n in [1..10]]; // Vincenzo Librandi, Dec 24 2011

CROSSREFS

Cf. A048922, A048923.

Sequence in context: A236008 A141815 A172701 * A183678 A251564 A066590

Adjacent sequences:  A048921 A048922 A048923 * A048925 A048926 A048927

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 | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified December 19 01:55 EST 2014. Contains 252175 sequences.