A127869 Number of L-shaped tiles in all tilings of a 3 X n board with 1 X 1 and L-shaped tiles (where the L-shaped tiles cover 3 squares).

12, 60, 432, 2348, 13144, 69280, 361012, 1841736, 9286900, 46303316, 228903592, 1123242916, 5477879120, 26572232312, 128302070508, 616985221280, 2956362520140, 14120605179500, 67252176519008, 319477138444252, 1514116534887688, 7160712605686480, 33799490762646948

Offset

2,1

Links

Table of n, a(n) for n=2..24.

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

Cf. A127864, A127865, A127866, A127867, A127868, A127870.

Sequence in context: A324946 A219738 A309308 * A012518 A012315 A009062

Adjacent sequences: A127866 A127867 A127868 * A127870 A127871 A127872

Keyword

nonn

Author

Silvia Heubach (sheubac(AT)calstatela.edu), Feb 03 2007

Status

approved