A247708 - OEIS

%I #12 Feb 06 2017 19:02:32

%S 1,1,5,39,16,1,369,120,12,2908,1000,98,19185,7474,1228,60,3,137200,

%T 63896,12448,1092,53,1022915,540562,120034,12676,590,4,7606043,

%U 4365686,1084022,140512,8836,250,5,55699672,34738058,9663366,1466724,124242,5984,166

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

%C Sum_{k>0} k * T(n,k) = A247741(n).

%H Alois P. Heinz, <a href="/A247708/b247708.txt">Rows n = 0..175, flattened</a>

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

%e T(3,2) = 1:

%e ._____.

%e | ._. |

%e |_| |_|

%e |_. ._|

%e | |_| |

%e |_____| .

%e Triangle T(n,k) begins:

%e 00 :        1;

%e 01 :        1;

%e 02 :        5;

%e 03 :       39,       16,       1;

%e 04 :      369,      120,      12;

%e 05 :     2908,     1000,      98;

%e 06 :    19185,     7474,    1228,      60,      3;

%e 07 :   137200,    63896,   12448,    1092,     53;

%e 08 :  1022915,   540562,  120034,   12676,    590,    4;

%e 09 :  7606043,  4365686, 1084022,  140512,   8836,  250,   5;

%e 10 : 55699672, 34738058, 9663366, 1466724, 124242, 5984, 166;

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

%Y Column k=0 gives A247772.

%Y Cf. A247741.

%K nonn,tabf

%O 0,3

%A _Alois P. Heinz_, Sep 22 2014