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

Index entries for linear recurrences with constant coefficients, signature (3, 7, -1, 2).

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}]

Prog

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; 2, -1, 7, 3]^n*[1; 1; 11; 39])[1, 1] \\ Charles R Greathouse IV, May 11 2026

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,easy

Author

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

Status

approved