OFFSET
1,1
COMMENTS
The identity (1250*n^2 + 100*n + 1)^2 - (25*n^2 + 2*n)*(250*n + 10)^2 = 1 can be written as a(n)^2 - A154377(n)*A154379(n)^2 = 1. - Vincenzo Librandi, Jan 30 2012
This is the case s=5 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 30 2012
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(1)=1351, a(2)=5201, a(3)=11551, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Apr 25 2011
G.f.: x*(x^2 + 1148*x + 1351)/(1-x)^3. - Vincenzo Librandi, Jan 30 2012
E.g.f.: (1250*x^2 + 1350*x + 1)*exp(x) - 1. - G. C. Greubel, Sep 15 2016
MATHEMATICA
Table[1250n^2+100n+1, {n, 30}] (* or *) LinearRecurrence[{3, -3, 1}, {1351, 5201, 11551}, 30] (* Harvey P. Dale, Apr 25 2011 *)
PROG
(PARI) a(n)=1250*n^2+100*n+1 \\ Charles R Greathouse IV, Dec 27 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jan 08 2009
EXTENSIONS
Minor corrections by M. F. Hasler, Oct 08 2014
STATUS
approved