A354131 - OEIS

%I #16 May 18 2022 13:13:17

%S 1,2,12,48,216,936,4104,17928,78408,342792,1498824,6553224,28652616,

%T 125277192,547747272,2394904968,10471198536,45783025416,200176267464,

%U 875226954888,3826738469448,16731577137672,73155162229704,319854949515144,1398495821923656

%N Number of tilings of a 2 X n rectangle using 2 X 2 and 1 X 1 tiles, right trominoes and dominoes.

%C Tiling algorithm see A351322.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,6).

%F G.f.: (1 - x) / (1 - 3*x - 6*x^2).

%F a(n) = 3*a(n-1) + 6*a(n-2).

%e a(3)=48

%e Number of tilings without a 2 X 2 square: 44, see A353878.

%e Number of other tilings: 4

%e    ___ _   ___ _   _ ___   _ ___

%e   |   | | |   |_| | |   | |_|   |

%e   |___|_| |___|_| |_|___| |_|___|

%o (Maxima), see A352589.

%Y Cf. A351322, A352589, A353878, A354130, A354132.

%K nonn,easy

%O 0,2

%A _Gerhard Kirchner_, May 18 2022