A247124 - OEIS

%I #17 Feb 06 2017 18:39:36

%S 1,1,1,2,3,8,14,21,37,63,122,221,374,656,1147,2066,3699,6477,11407,

%T 20099,35656,63323,111775,197352,348556,616560,1091570,1929721,

%U 3410509,6028021,10658114,18851012,33331681,58927069,104177155,184188343,325686763,575858676

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

%H Alois P. Heinz, <a href="/A247124/b247124.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.: see Maple program.

%e a(4) = 3:

%e ._______.   ._______.   ._______.

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

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

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

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

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

%p gf:= -(x-1)^2 *(x^4+x^3+x^2+x+1)^2 /

%p      (x^15 +x^13 +x^11 -3*x^10 -2*x^8 -2*x^6 +6*x^5 +x^3 +x-1):

%p a:= n-> coeff(series(gf, x, n+1), x, n):

%p seq(a(n), n=0..50);

%Y Cf. A174249, A233427, A247125, A247268, A264812.

%K nonn

%O 0,4

%A _Alois P. Heinz_, Nov 19 2014