A234931 - OEIS

%I #14 Feb 06 2017 17:45:58

%S 1,0,0,0,2,0,0,0,4,0,8,0,16,0,40,0,64,16,200,96,504,464,1528,1664,

%T 4376,5616,12792,18192,38264,58384,115832,186368,355808,589344,

%U 1095408,1853664,3383656,5802016,10470376,18125280,32461312,56552736,100782696,176318464

%N Number of tilings of a 5 X n rectangle using n pentominoes of shapes F, U, N.

%H Alois P. Heinz, <a href="/A234931/b234931.txt">Table of n, a(n) for n = 0..1000</a>

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

%F G.f.: (4*x^20 +4*x^18 +8*x^16 -3*x^14 +4*x^13 -5*x^12 -2*x^11 +3*x^10 -2*x^9 +6*x^8 -2*x^7 +2*x^6 -2*x^5 -x^4 +2*x -1) / (-8*x^22 -28*x^20 -6*x^18 +8*x^17 +26*x^16 +4*x^15 +7*x^14 -8*x^13 -9*x^12 -14*x^11 +7*x^10 +2*x^9 +8*x^8 -2*x^7 +2*x^6 -6*x^5 +x^4 +2*x -1).

%e a(4) = 2:

%e ._______.   ._______.

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

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

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

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

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

%Y Cf. A174249, A233427, A234312, A247680, A247126.

%K nonn

%O 0,5

%A _Alois P. Heinz_, Jan 01 2014