A247705 - OEIS

%I #15 Feb 07 2017 10:15:32

%S 1,1,5,48,8,423,68,10,3082,832,84,8,18998,7624,1230,88,10,133083,

%T 65360,14390,1732,116,8,965175,555236,150876,23184,2196,108,6,6907447,

%U 4531744,1454292,275320,33807,2616,124,4,48357538,36466396,13354738,3012116,457360,46872,3086,104,2

%N Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape N; triangle T(n,k), n>=0, read by rows.

%C Sum_{k>0} k * T(n,k) = A247738(n).

%H Alois P. Heinz, <a href="/A247705/b247705.txt">Rows n = 0..160, flattened</a>

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

%e T(3,1) = 8:

%e ._____.        .___._.

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

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

%e | ._| |        | | | |

%e | |   |        |_|_| |

%e |_|___| (*4)   |_____| (*4)  .

%e Triangle T(n,k) begins:

%e 00 :      1;

%e 01 :      1;

%e 02 :      5;

%e 03 :     48,      8;

%e 04 :    423,     68,     10;

%e 05 :   3082,    832,     84,     8;

%e 06 :  18998,   7624,   1230,    88,   10;

%e 07 : 133083,  65360,  14390,  1732,  116,   8;

%e 08 : 965175, 555236, 150876, 23184, 2196, 108,  6;

%Y Row sums give A174249 or A233427(n,5).

%Y Column k=0 gives A247769.

%Y Cf. A247738.

%K nonn,tabf

%O 0,3

%A _Alois P. Heinz_, Sep 22 2014