OFFSET
0,2
COMMENTS
a(n)/a(n-1) tends to (7+sqrt(13))/2 = 5.30277563... = 2+A098316.
For n >= 2, a(n) equals 3^n times the permanent of the (2n-2) X (2n-2) matrix with 1/sqrt(3)'s along the main diagonal, and 1's along the superdiagonal and the subdiagonal. - John M. Campbell, Jul 08 2011
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..100
Index entries for linear recurrences with constant coefficients, signature (7,-9).
FORMULA
G.f.: (1-4x)/(1-7x+9x^2).
a(n) = Sum_{k=0..n} A165253(n,k)*3^(n-k).
a(n) = ((13-sqrt(13))*(7+sqrt(13))^n+(13+sqrt(13))*(7-sqrt(13))^n )/(26*2^n). - Klaus Brockhaus, Sep 26 2009
MATHEMATICA
LinearRecurrence[{7, -9}, {1, 3}, 30] (* Harvey P. Dale, Sep 23 2011 *)
PROG
(Magma) I:=[1, 3]; [n le 2 select I[n] else 7*Self(n-1)-9*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Sep 24 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
Philippe Deléham, Sep 14 2009
STATUS
approved