%I #18 May 07 2024 08:44:51

%S 1,1,1,1,1,2,3,6,9,12,16,21,41,66,106,156,219,364,558,930,1444,2191,

%T 3515,5361,8737,13661,21478,34397,53528,86137,135294,215432,345081,

%U 546705,879212,1395476,2239086,3596427,5767656,9312008,14949738,24163742,39045229

%N Number of tilings of a 5 X n rectangle using n pentominoes of shapes T, W, I, X.

%H Alois P. Heinz, <a href="/A372221/b372221.txt">Table of n, a(n) for n = 0..4472</a>

%H Alois P. Heinz, <a href="/A372221/a372221.txt">G.f. for A372221</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>

%H <a href="/index/Rec#order_139">Index entries for linear recurrences with constant coefficients</a>, order 139.

%e a(7) = 6:

%e ._____________. ._____________. ._____________.

%e | |_________| | | | | | | | | | |_________| | |

%e | .___| |___. | | | | | | | | | |_________| | |

%e |_| ._| |_. |_| | | | | | | | | |_________| | |

%e | ._|_____|_. | | | | | | | | | |_________| | |

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

%e ._____________. ._____________. ._____________.

%e | |_________| | | |_________| | | | |_________|

%e |_. |_. ._| ._| | |_________| | | | |_________|

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

%e | .___|_|___. | | |_________| | | | |_________|

%e |_|_________|_| |_|_________|_| |_|_|_________| .

%Y Cf. A003520, A174249, A366324.

%K nonn,easy

%O 0,6

%A _Alois P. Heinz_, Apr 22 2024