A127870 Number of tilings of a 4 X n board with 1 X 1 and L-shaped tiles (where the L-shaped tiles cover 3 squares).

1, 1, 33, 195, 2023, 16839, 151817, 1328849, 11758369, 103628653, 914646205, 8068452381, 71189251649, 628067760289, 5541284098945, 48888866203241, 431331449340441, 3805499681885145, 33574725778806817, 296219181642118401, 2613448287490035073

Offset: 0

Author

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

Keywords

• nonn

Examples

			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.
		

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).

Crossrefs

Cf. A127864, A127865, A127866, A127867, A127868, A127869.

Column k=4 of A220054. - Alois P. Heinz, Dec 03 2012

Programs

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}]

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).