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A158602 a(n) = 40*n^2 + 1. 2
1, 41, 161, 361, 641, 1001, 1441, 1961, 2561, 3241, 4001, 4841, 5761, 6761, 7841, 9001, 10241, 11561, 12961, 14441, 16001, 17641, 19361, 21161, 23041, 25001, 27041, 29161, 31361, 33641, 36001, 38441, 40961, 43561, 46241, 49001, 51841, 54761, 57761, 60841, 64001 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The identity (40*n^2 + 1)^2 - (400*n^2 + 20)*(2*n)^2 = 1 can be written as a(n)^2 - A158601(n)*A005843(n)^2 = 1.
LINKS
Vincenzo Librandi, X^2-AY^2=1, Math Forum, 2007. [Wayback Machine link]
FORMULA
G.f.: -(1 + 38*x + 41*x^2)/(x-1)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
From Amiram Eldar, Mar 16 2023: (Start)
Sum_{n>=0} 1/a(n) = (coth(Pi/(2*sqrt(10)))*Pi/(2*sqrt(10)) + 1)/2.
Sum_{n>=0} (-1)^n/a(n) = (cosech(Pi/(2*sqrt(10)))*Pi/(2*sqrt(10)) + 1)/2. (End)
MAPLE
A158602:=n->40*n^2; seq(A158602(k), k=0..100); # Wesley Ivan Hurt, Sep 27 2013
MATHEMATICA
40*Range[0, 40]^2+1 (* or *) LinearRecurrence[{3, -3, 1}, {1, 41, 161}, 40] (* Harvey P. Dale, Jul 25 2011 *)
Table[40n^2+1, {n, 0, 100}] (* Wesley Ivan Hurt, Sep 27 2013 *)
PROG
(Magma) I:=[1, 41, 161]; [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 16 2012
(PARI) for(n=0, 40, print1(40*n^2 + 1", ")); \\ Vincenzo Librandi, Feb 16 2012
CROSSREFS
Sequence in context: A105100 A141988 A347075 * A245743 A142839 A142912
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 22 2009
EXTENSIONS
Comment rewritten, formula replaced by R. J. Mathar, Oct 28 2009
STATUS
approved

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Last modified May 27 16:57 EDT 2024. Contains 372880 sequences. (Running on oeis4.)