OFFSET
0,2
COMMENTS
Subsequence of A160842. - Bruno Berselli, Feb 06 2012
The identity (25*n^2 + 1)^2 - (25*n^2 + 2)*(5*n)^2 = 1 can be written as (A016850(n+1) + 1)^2 - a(n+1)*A008587(n+1)^2 = 1. - Vincenzo Librandi, Feb 08 2012
LINKS
Bruno Berselli, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: (1+x)*(1 + 23*x + x^2)/(1-x)^3. - Bruno Berselli, Feb 06 2012
E.g.f.: (x*(x+1)*25 + 2)*e^x - 1. - Gopinath A. R., Feb 14 2012
Sum_{n>=0} 1/a(n) =3/4+sqrt(2)/20*Pi*coth(Pi*sqrt(2)/5) = 1.062575323280590.. - R. J. Mathar, May 07 2024
MATHEMATICA
Join[{1}, 25 Range[40]^2 + 2] (* Bruno Berselli, Feb 06 2012 *)
Join[{1}, LinearRecurrence[{3, -3, 1}, {27, 102, 227}, 50]] (* Vincenzo Librandi, Feb 08 2012 *)
PROG
(PARI) A010015(n)=25*n^2+2-!n \\ M. F. Hasler, Feb 14 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved