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!)
A158731 a(n) = 1156*n^2 + 34. 2
34, 1190, 4658, 10438, 18530, 28934, 41650, 56678, 74018, 93670, 115634, 139910, 166498, 195398, 226610, 260134, 295970, 334118, 374578, 417350, 462434, 509830, 559538, 611558, 665890, 722534, 781490, 842758, 906338, 972230, 1040434, 1110950, 1183778, 1258918 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
The identity (68*n^2 + 1)^2 - (1156*n^2 + 34)*(2*n)^2 = 1 can be written as A158732(n)^2 - a(n)*A005843(n)^2 = 1.
LINKS
Vincenzo Librandi, X^2-AY^2=1, Math Forum, 2007. [Wayback Machine link]
FORMULA
G.f.: -34*(1 + 32*x + 35*x^2)/(x-1)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
From Amiram Eldar, Mar 22 2023: (Start)
Sum_{n>=0} 1/a(n) = (coth(Pi/sqrt(34))*Pi/sqrt(34) + 1)/68.
Sum_{n>=0} (-1)^n/a(n) = (cosech(Pi/sqrt(34))*Pi/sqrt(34) + 1)/68. (End)
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {34, 1190, 4658}, 50] (* Vincenzo Librandi, Feb 20 2012 *)
PROG
(Magma) I:=[34, 1190, 4658]; [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, Feb 20 2012
(PARI) for(n=0, 40, print1(1156*n^2 + 34", ")); \\ Vincenzo Librandi, Feb 20 2012
CROSSREFS
Sequence in context: A189434 A167258 A251924 * A297693 A093550 A296587
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 25 2009
EXTENSIONS
Comment rewritten, a(0) added and formula replaced by R. J. Mathar, Oct 22 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 March 29 08:01 EDT 2024. Contains 371265 sequences. (Running on oeis4.)