OFFSET
0,1
COMMENTS
The identity (81*n^2 + 90*n + 26)^2 - (9*n^2 + 10*n + 3)*(27*n + 15)^2 = 1 can be written as A154277(n+1)^2 - A154254(n+1)*a(n)^2 = 1. - Vincenzo Librandi, Feb 03 2012
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
G.f.: 3*(5 + 4*x)/(1-x)^2. - R. J. Mathar, Jan 05 2011
a(n) = 3*A017221(n). - R. J. Mathar, Jan 05 2011
a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Feb 02 2012
E.g.f.: (27*x + 15)*exp(x). - G. C. Greubel, Sep 08 2016
MATHEMATICA
Range[15, 7000, 27] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)
LinearRecurrence[{2, -1}, {15, 42}, 40] (* Vincenzo Librandi, Feb 02 2012 *)
27*Range[0, 50]+15 (* Harvey P. Dale, Feb 26 2017 *)
PROG
(PARI) a(n)=27*n+15 \\ Charles R Greathouse IV, Dec 28 2011
(Magma) I:=[15, 42]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 02 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jan 06 2009
STATUS
approved