OFFSET
0,3
COMMENTS
For n>=2, a(n) equals the permanent of the (n-1) X (n-1) tridiagonal matrix with 4's along the main diagonal, and 3's along the superdiagonal and the subdiagonal. - John M. Campbell, Jul 19 2011
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,9).
FORMULA
From R. J. Mathar, Apr 29 2008: (Start)
O.g.f.: x/(1-4*x-9*x^2).
a(n) = -9^n*(A^n - B^n)/(2*sqrt(13)) where A = -1/(2+sqrt(13)) and B = 1/(sqrt(13)-2). (End)
a(n) = Sum_{k, 0<=k<=n} A155161(n,k)*3^(n-k), n>=1. - Philippe Deléham, Jan 27 2009
MATHEMATICA
a[n_]:=(MatrixPower[{{1, 4}, {1, -5}}, n].{{1}, {1}})[[2, 1]]; Table[Abs[a[n]], {n, -1, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2010 *)
LinearRecurrence[{4, 9}, {0, 1}, 30] (* Vincenzo Librandi, Nov 12 2012 *)
PROG
(Sage) [lucas_number1(n, 4, -9) for n in range(0, 22)] # Zerinvary Lajos, Apr 23 2009
(Magma) [n le 2 select n-1 else 4*Self(n-1)+9*Self(n-2): n in [1..30] ]; // Vincenzo Librandi, Nov 12 2012
(PARI) x='x+O('x^30); concat([0], Vec(x/(1-4*x-9*x^2))) \\ G. C. Greubel, Jan 01 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved