The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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!)
A157509 a(n) = 13122*n^2 - 324*n + 1. 3
12799, 51841, 117127, 208657, 326431, 470449, 640711, 837217, 1059967, 1308961, 1584199, 1885681, 2213407, 2567377, 2947591, 3354049, 3786751, 4245697, 4730887, 5242321, 5779999, 6343921, 6934087, 7550497, 8193151, 8862049 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The identity (13122*n^2 - 324*n + 1)^2 - (81*n^2 - 2*n)*(1458*n - 18)^2 = 1 can be written as a(n)^2 - A157507(n)* A157508(n)^2 = 1. - Vincenzo Librandi, Jan 26 2012
This is the case s=9 of the identity (2*s^4*n^2 - 4*s^2*n + 1)^2 - (s^2*n^2 - 2*n)*(2*s^3*n - 2*s)^2 = 1. - Bruno Berselli, Jan 26 2011
LINKS
Vincenzo Librandi, X^2-AY^2=1
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 26 2012
G.f.: x*(-12799 - 13444*x - x^2)/(x-1)^3. - Vincenzo Librandi, Jan 26 2012
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {12799, 51841, 117127}, 40] (* Vincenzo Librandi, Jan 26 2012 *)
Table[13122n^2-324n+1, {n, 30}] (* Harvey P. Dale, Jun 30 2022 *)
PROG
(Magma) I:=[12799, 51841, 117127]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jan 26 2012
(PARI) for(n=1, 22, print1(13122n^2 - 324n + 1", ")); \\ Vincenzo Librandi, Jan 26 2012
CROSSREFS
Sequence in context: A206966 A209091 A207133 * A035916 A243050 A246809
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 02 2009
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 June 12 17:51 EDT 2024. Contains 373359 sequences. (Running on oeis4.)