OFFSET
0,2
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..900
Index entries for linear recurrences with constant coefficients, signature (21,-108).
FORMULA
a(n) = (12^(n+1) - 9^(n+1))/3. - Lambert Klasen (lambert.klasen(AT)gmx.net), Feb 05 2005
a(n-1) = Sum_{k=1..n} 3^(n-1)*3^(n-k)*binomial(n,k). - Zerinvary Lajos, Sep 24 2006
From Vincenzo Librandi, Feb 09 2011: (Start)
a(n) = 12*a(n-1) + 9^n, a(0)=1.
a(n) = 21*a(n-1) - 108*a(n-2); a(0)=1, a(1)=21. (End)
E.g.f.: exp(9*x)*(4*exp(3*x) - 3). - Elmo R. Oliveira, Mar 31 2025
MATHEMATICA
CoefficientList[Series[1/((1-9x)(1-12x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{21, -108}, {1, 21}, 30] (* Harvey P. Dale, Oct 15 2011 *)
PROG
(PARI) Vec(1/((1-9*x)*(1-12*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved