A127867 Number of tilings of a 3 X n board with 1 X 1 and L-shaped tiles (where the L-shaped tiles cover 3 squares).

1, 1, 11, 39, 195, 849, 3895, 17511, 79339, 358397, 1620843, 7326991, 33127155, 149766353, 677103839, 3061202815, 13839823275, 62570318397, 282882722979, 1278922980071, 5782057329219, 26140890761969, 118183916056327, 534313772133687, 2415651952691819

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

Formula

G.f.: (1-x)^2/(1-3x-7x^2+x^3-2x^4).

Example

a(2) = 11 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.

Mathematica

Table[Coefficient[Normal[Series[(1 - x)^2/(1 - 3x - 7x^2 + x^3 - 2x^4), {x, 0, 30}]], x, n], {n, 0, 30}]

Crossrefs

Cf. A127864, A127865, A127866, A127868, A127869, A127870.

Column k=3 of A220054. - Alois P. Heinz, Dec 03 2012

Sequence in context: A343124 A336901 A173373 * A138050 A341232 A183940

Adjacent sequences: A127864 A127865 A127866 * A127868 A127869 A127870

Keyword

nonn

Author

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

Status

approved