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%I #14 Dec 18 2022 12:08:53
%S 1,1,11,39,195,849,3895,17511,79339,358397,1620843,7326991,33127155,
%T 149766353,677103839,3061202815,13839823275,62570318397,282882722979,
%U 1278922980071,5782057329219,26140890761969,118183916056327,534313772133687,2415651952691819
%N 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).
%H Alois P. Heinz, <a href="/A127867/b127867.txt">Table of n, a(n) for n = 0..500</a>
%H P. Chinn, R. Grimaldi and S. Heubach, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL10/Heubach/heubach40.html">Tiling with L's and Squares</a>, Journal of Integer Sequences, Vol. 10 (2007), Article 07.2.8
%F G.f.: (1-x)^2/(1-3x-7x^2+x^3-2x^4).
%e 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.
%t Table[Coefficient[Normal[Series[(1 - x)^2/(1 - 3x - 7x^2 + x^3 - 2x^4), {x, 0, 30}]], x, n], {n, 0, 30}]
%Y Cf. A127864, A127865, A127866, A127868, A127869, A127870.
%Y Column k=3 of A220054. - _Alois P. Heinz_, Dec 03 2012
%K nonn
%O 0,3
%A Silvia Heubach (sheubac(AT)calstatela.edu), Feb 03 2007
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