OFFSET
2,1
LINKS
P. Z. Chinn, R. Grimaldi and S. Heubach, Tiling with Ls and Squares, J. Int. Sequences 10 (2007) #07.2.8.
S. Heubach, Tiling with Ls and Squares, 2005.
Index entries for linear recurrences with constant coefficients, signature (6,5,-44,-39,2,-29,4,-4).
FORMULA
G.f.: 4*x^2*(x-1)*(x^3-3*x^2-3)/(1-3*x-7*x^2+x^3-2*x^4)^2.
EXAMPLE
a(2) = 12 because the 3 X 2 board can be tiled in one way with only square tiles, in 8 ways using one L-tile and 3 square tiles and in 2 ways with 2 L-tiles, so there are altogether 8 + 2*2 = 12 L-tiles in all of the 3 X 2 tilings.
MATHEMATICA
Table[Coefficient[Normal[Series[4x^2(3-3x+3x^2-4x^3+x^4)/(1-3x-7x^2+x^3-2x^4)^2, {x, 0, 30}]], x, n], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Silvia Heubach (sheubac(AT)calstatela.edu), Feb 03 2007
STATUS
approved