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!)
A157912 a(n) = 64*n^2 + 16. 2
80, 272, 592, 1040, 1616, 2320, 3152, 4112, 5200, 6416, 7760, 9232, 10832, 12560, 14416, 16400, 18512, 20752, 23120, 25616, 28240, 30992, 33872, 36880, 40016, 43280, 46672, 50192, 53840, 57616, 61520, 65552, 69712, 74000, 78416, 82960, 87632, 92432, 97360, 102416 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The identity (8*n^2+1)^2 - (64*n^2+16)*n^2 = 1 can be written as A081585(n)^2 - a(n)*n^2 = 1. - Vincenzo Librandi, Feb 09 2012
LINKS
Vincenzo Librandi, X^2-AY^2=1, Math Forum, 2007. [Wayback Machine link]
FORMULA
From Vincenzo Librandi, Feb 09 2012: (Start)
G.f.: x*(80+32*x+16*x^2)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
From Amiram Eldar, Mar 07 2023: (Start)
Sum_{n>=1} 1/a(n) = (coth(Pi/2)*Pi/2 - 1)/32.
Sum_{n>=1} (-1)^(n+1)/a(n) = (1 - cosech(Pi/2)*Pi/2)/32. (End)
MAPLE
A157912:=n->64*n^2 + 16: seq(A157912(n), n=1..50); # Wesley Ivan Hurt, Oct 27 2014
MATHEMATICA
64Range[50]^2+16 (* Harvey P. Dale, Mar 24 2011 *)
LinearRecurrence[{3, -3, 1}, {80, 272, 592}, 40] (* Vincenzo Librandi, Feb 09 2012 *)
PROG
(Magma) I:=[80, 272, 592]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 09 2012
(PARI) for(n=1, 40, print1(64*n^2 + 16", ")); \\ Vincenzo Librandi, Feb 09 2012
CROSSREFS
Cf. A081585.
Sequence in context: A235091 A306434 A234890 * A234883 A194646 A057441
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 09 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 February 28 13:24 EST 2024. Contains 370399 sequences. (Running on oeis4.)