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A127864 Number of tilings of a 2xn board with 1x1 and L-shaped tiles (where the L-shaped tiles cover 3 squares). 13
1, 1, 5, 11, 33, 87, 241, 655, 1793, 4895, 13377, 36543, 99841, 272767, 745217, 2035967, 5562369, 15196671, 41518081, 113429503, 309895169, 846649343, 2313089025, 6319476735, 17265131521, 47169216511, 128868696065, 352075825151, 961889042433, 2627929735167 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The signed version of this sequence appears as A077917.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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.

Index entries for linear recurrences with constant coefficients, signature (1, 4, 2).

FORMULA

a(n) = a(n-1)+ 4 a(n-2) + 2 a(n-3); a(n) = (-1)^n +(1/Sqrt(3))*((1+Sqrt(3))^n - (1-Sqrt(3))^n).

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

a(n) = A028860(n+2)+(-1)^n. - R. J. Mathar, Oct 29 2010

EXAMPLE

a(2) = 5 because the 2 X 2 board can be tiled either with 4 squares or with a single L-shaped tile (in four orientations) together with a single square tile.

MATHEMATICA

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

CROSSREFS

Cf. A077917, A127865, A127866, A127867, A127868, A127869, A127870, A127871, A127872.

Column k=2 of A220054. - Alois P. Heinz, Dec 03 2012

Sequence in context: A107442 A280540 A077917 * A055936 A194589 A189918

Adjacent sequences:  A127861 A127862 A127863 * A127865 A127866 A127867

KEYWORD

easy,nonn

AUTHOR

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

EXTENSIONS

JIS reference updated by R. J. Mathar, Oct 30 2010

STATUS

approved

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Last modified June 27 04:02 EDT 2017. Contains 288777 sequences.