OFFSET
0,2
COMMENTS
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-10,3).
FORMULA
G.f.: (2*x-1)/((3*x-1)*(x^2-3*x+1)). Define c = (3+sqrt(5))/2 and d = (3-sqrt(5))/2. Then a(n) = 3^(n+1) - ((2*sqrt(5)/5)+1)*c^n + ((2*sqrt(5)/5)-1)*d^n = 3^(n+1) - Fibonacci(2n+3). - Ralf Stephan, May 20 2007
MATHEMATICA
LinearRecurrence[{6, -10, 3}, {1, 4, 14}, 30] (* Harvey P. Dale, May 07 2017 *)
PROG
(Magma) [3^(n+1) - Fibonacci(2*n+3): n in [0..30]]; // Vincenzo Librandi, Apr 21 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Creighton Dement, Apr 19 2005
EXTENSIONS
Comment concerning the binomial transforms corrected by R. J. Mathar, Oct 26 2009
STATUS
approved