login
Number of tilings of a 5 X n rectangle using dominoes and straight (3 X 1) trominoes.
3

%I #9 Dec 07 2012 12:45:27

%S 1,2,15,143,1069,9612,82634,707903,6155230,53074167,458901955,

%T 3968548571,34293794622,296497719200,2563023778341,22155553744380,

%U 191528023181443,1655649630655481,14312296720331975,123722938782920490,1069522524403416934,9245501816227527991

%N Number of tilings of a 5 X n rectangle using dominoes and straight (3 X 1) trominoes.

%H Alois P. Heinz, <a href="/A219868/b219868.txt">Table of n, a(n) for n = 0..500</a>

%e a(2) = 15, because there are 15 tilings of a 5 X 2 rectangle using dominoes and straight (3 X 1) trominoes:

%e .___. .___. .___. .___. .___. .___. .___. .___.

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

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

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

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

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

%e .___. .___. .___. .___. ._._. ._._. .___.

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

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

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

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

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

%Y Column k=5 of A219866.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Nov 30 2012