OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..550
Index entries for linear recurrences with constant coefficients, signature (2,6,-4,11,2).
FORMULA
G.f.: (2*x^4 - 2*x^3 + x^2 + 2*x - 1) / (2*x^5 + 11*x^4 - 4*x^3 + 6*x^2 + 2*x - 1).
a(0)=1, a(1)=0, a(2)=5, a(3)=8, a(4)=55, a(n) = 2*a(n-1) + 6*a(n-2) - 4*a(n-3) + 11*a(n-4) + 2*a(n-5). - Harvey P. Dale, Mar 19 2013
EXAMPLE
a(2) = 5, because there are 5 tilings of a 3 X 2 rectangle using dominoes and right trominoes:
.___. .___. ._._. .___. .___.
|___| |_._| | | | | ._| |_. |
|___| | | | |_|_| |_| | | |_|
|___| |_|_| |___| |___| |___|
MAPLE
a:= n-> (Matrix([[55, 8, 5, 0, 1]]). Matrix(5, (i, j)-> if i=j-1 then 1 elif j=1 then [2, 6, -4, 11, 2][i] else 0 fi)^n)[1, 5]: seq(a(n), n=0..25);
MATHEMATICA
a[n_] := Last[{55, 8, 5, 0, 1} . MatrixPower[ Table[ Which[i == j - 1, 1, j == 1, {2, 6, -4, 11, 2}[[i]], True, 0], {i, 1, 5}, {j, 1, 5}], n]]; Table[a[n], {n, 0, 24}] (* Jean-François Alcover, Jul 19 2012, translated from Maple *)
LinearRecurrence[{2, 6, -4, 11, 2}, {1, 0, 5, 8, 55}, 30] (* Harvey P. Dale, Mar 19 2013 *)
CROSSREFS
KEYWORD
easy,nice,nonn
AUTHOR
Alois P. Heinz, Sep 24 2009
STATUS
approved