A247708 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.

1, 1, 5, 39, 16, 1, 369, 120, 12, 2908, 1000, 98, 19185, 7474, 1228, 60, 3, 137200, 63896, 12448, 1092, 53, 1022915, 540562, 120034, 12676, 590, 4, 7606043, 4365686, 1084022, 140512, 8836, 250, 5, 55699672, 34738058, 9663366, 1466724, 124242, 5984, 166

Offset: 0

Author

Alois P. Heinz, Sep 22 2014

Keywords

• nonn
• tabf

Comments

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

Examples

			T(3,2) = 1:
._____.
| ._. |
|_| |_|
|_. ._|
| |_| |
|_____| .
Triangle T(n,k) begins:
00 :        1;
01 :        1;
02 :        5;
03 :       39,       16,       1;
04 :      369,      120,      12;
05 :     2908,     1000,      98;
06 :    19185,     7474,    1228,      60,      3;
07 :   137200,    63896,   12448,    1092,     53;
08 :  1022915,   540562,  120034,   12676,    590,    4;
09 :  7606043,  4365686, 1084022,  140512,   8836,  250,   5;
10 : 55699672, 34738058, 9663366, 1466724, 124242, 5984, 166;
		

Links

• Alois P. Heinz, Rows n = 0..175, flattened
• Wikipedia, Pentomino

Crossrefs

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

Column k=0 gives A247772.

Cf. A247741.