OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,5,6,4,0,-1,0,-3,-2,-4,0,-2).
FORMULA
G.f.: (x^6+2*x^2-1) / (-2*x^12 -4*x^10 -2*x^9 -3*x^8 -x^6 +4*x^4 +6*x^3 +5*x^2-1).
EXAMPLE
a(3) = 6:
._____. ._____. .___._. ._.___. ._____. ._____.
| .___| |___. | | | | | | | |___. | | .___|
|_|_. | | ._|_| |___| | | |___| | |_| |_| |
| | | | | | | |___| |___| | |___| | | |___|
|___|_| |_|___| |_____| |_____| |_____| |_____|
MAPLE
a:= n-> (Matrix(12, (i, j)-> `if`(i+1=j, 1, `if`(i=12,
[-2, 0, -4, -2, -3, 0, -1, 0, 4, 6, 5, 0][j], 0)))^(n+8).
<<-1, 0, 1/2, [0$5][], 1, 0, 3, 6>>)[1, 1]:
seq(a(n), n=0..40);
MATHEMATICA
a[n_] := MatrixPower[ Table[ If[i+1 == j, 1, If[i == 12, {-2, 0, -4, -2, -3, 0, -1, 0, 4, 6, 5, 0}[[j]], 0]], {i, 1, 12}, {j, 1, 12}], n+8].{-1, 0, 1/2, 0, 0, 0, 0, 0, 1, 0, 3, 6} // First; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Dec 05 2013, after Maple *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Jun 03 2013
STATUS
approved