OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..500
P. Chinn, R. Grimaldi and S. Heubach, Tiling with L's and Squares, Journal of Integer Sequences, Vol. 10 (2007), Article 07.2.8
Index entries for linear recurrences with constant coefficients, signature (5, 34, 6, -72, -28, 74, -10, -4, -4).
FORMULA
G.f.: (1 - 4 z - 6 z^2 - 10 z^3 - 8 z^4 - 4 z^5) / (1 - 5z - 34 z^2 - 6 z^3 + 72 z^4 + 28 z^5 - 74 z^6 + 10 z^7 + 4 z^8 + 4 z^9).
EXAMPLE
a(2) = 33 because the 4x2 board can be tiled in one way with only square tiles, in 12 ways using one L-tile and 5 square tiles and in 20 ways with 2 L-tiles and 2 square tiles.
MATHEMATICA
Table[Coefficient[Normal[Series[(1 - 4 z - 6 z^2 - 10 z^3 - 8 z^4 - 4 z^5)/(1 - 5z - 34 z^2 - 6 z^3 + 72 z^4 + 28 z^5 - 74 z^6 + 10 z^7 + 4 z^8 + 4 z^9), {x, 0, 30}]], x, n], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Silvia Heubach (sheubac(AT)calstatela.edu), Feb 03 2007
STATUS
approved