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!)
A048916 Indices of 9-gonal numbers which are also hexagonal. 3
1, 10, 39025, 621946, 2517635809, 40124201194, 162422756519761, 2588572715184730, 10478541711598202305, 166999180107303446986, 676012639819623666961969, 10773785102854001863647034 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
As n increases, the ratio of consecutive terms settles into an approximate 2-cycle with the ratio a(n)/a(n-1) bounded above and below by 2024+765*sqrt(7) and 8+3*sqrt(7) respectively. - Ant King, Dec 29 2011
LINKS
Eric Weisstein's World of Mathematics, Nonagonal Hexagonal Number
FORMULA
G.f.: -x*(1+9*x-25499*x^2+2295*x^3+154*x^4) / ((x-1)*(x^2-254*x+1)*(x^2+254*x+1)). - R. J. Mathar, Dec 21 2011
From Ant King, Dec 29 2011: (Start)
a(n) = 64514*a(n-2)-a(n-4)-23040.
a(n) = 1/28*(3*((3-sqrt(7)*(-1)^n)*(8+3*sqrt(7))^(2*n-2)+(3+sqrt(7)*(-1)^n)*(8-3*sqrt(7))^(2*n-2))+10).
a(n) = ceiling(3/28*(3-sqrt(7)*(-1)^n)*(8+3*sqrt(7))^(2*n-2)). (End)
MATHEMATICA
LinearRecurrence[{1, 64514, -64514, -1, 1}, {1, 10, 39025, 621946, 2517635809}, 210] (* Vincenzo Librandi, Dec 28 2011 *)
CROSSREFS
Sequence in context: A360213 A055321 A092300 * A366313 A260797 A055310
KEYWORD
nonn,easy
AUTHOR
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 March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)