OFFSET
0,1
COMMENTS
Also: inverse binomial transform of A135520. - R. J. Mathar, Apr 17 2008
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,3).
FORMULA
From R. J. Mathar, Feb 23 2008: (Start)
O.g.f.: (5/(1-3*x) + 3/(1+x))/4.
a(n) = (5*3^n + 3*(-1)^n)/4. (End)
G.f.: (x-2)/(3*x^2 + 2*x - 1). - Harvey P. Dale, Mar 14 2011
E.g.f.: (1/4)*(5*exp(3*x) + 3*exp(-x)). - G. C. Greubel, Oct 17 2016
MATHEMATICA
f[n_]:=3/(n+2); x=2; Table[x=f[x]; Numerator[x], {n, 0, 5!}] (* Vladimir Joseph Stephan Orlovsky, Mar 11 2010 *)
Transpose[NestList[Join[Rest[#], ListCorrelate[{3, 2}, #]]&, {2, 3}, 30]][[1]] (* Harvey P. Dale, Mar 14 2011 *)
CoefficientList[Series[(x-2)/(3x^2+2x-1), {x, 0, 30}], x] (* Harvey P. Dale, Mar 14 2011 *)
PROG
(PARI) a(n)=(5*3^n+3*(-1)^n)/4 \\ Charles R Greathouse IV, Jun 01 2011
(Magma) [(5*3^n+3*(-1)^n)/4: n in [0..40]]; // Vincenzo Librandi, Jun 02 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Feb 19 2008
EXTENSIONS
More terms from R. J. Mathar, Feb 23 2008
STATUS
approved