A247711 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape X; triangle T(n,k), n>=0, read by rows.

1, 1, 5, 55, 1, 493, 8, 3930, 76, 27207, 734, 9, 207118, 7414, 157, 1622723, 71986, 2064, 8, 12544364, 638499, 22232, 259, 95912510, 5558790, 222964, 3898, 50, 732066083, 47971603, 2179607, 49537, 948, 8, 5616480627, 410502410, 20604626, 564498, 13889, 180

Offset: 0

Author

Alois P. Heinz, Sep 23 2014

Keywords

• nonn
• tabf

Comments

Sum_{k>0} k * T(n,k) = A247744(n).

Examples

			T(3,1) = 1:
._____.
| ._. |
|_| |_|
|_. ._|
| |_| |
|_____|
.
Triangle T(n,k) begins:
00 :        1;
01 :        1;
02 :        5;
03 :       55,       1;
04 :      493,       8;
05 :     3930,      76;
06 :    27207,     734,      9;
07 :   207118,    7414,    157;
08 :  1622723,   71986,   2064,    8;
09 : 12544364,  638499,  22232,  259;
10 : 95912510, 5558790, 222964, 3898, 50;
		

Links

• Alois P. Heinz, Rows n = 0..185, flattened
• Wikipedia, Pentomino

Crossrefs

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

Columns k=0-1 give: A247775, A247828.

Cf. A247744.