A247703 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape I; triangle T(n,k), n>=0, 0<=k<=n, read by rows.

1, 0, 1, 4, 0, 1, 47, 8, 0, 1, 394, 94, 12, 0, 1, 2082, 1608, 282, 32, 0, 2, 15113, 8812, 3452, 512, 58, 0, 3, 111664, 73863, 22310, 5962, 790, 96, 0, 4, 789930, 631700, 218608, 45762, 9374, 1260, 142, 0, 5, 5388729, 5157928, 2067811, 491868, 81720, 15272, 1824, 196, 0, 6

Offset: 0

Author

Alois P. Heinz, Sep 22 2014

Keywords

• nonn
• tabl

Comments

Sum_{k>0} k * T(n,k) = A247736(n).

Examples

			T(5,5) = 2:
._._._._._.   ._________.
| | | | | |   |_________|
| | | | | |   |_________|
| | | | | |   |_________|
| | | | | |   |_________|
|_|_|_|_|_|   |_________| .
Triangle T(n,k) begins:
00 :      1;
01 :      0,      1;
02 :      4,      0,      1;
03 :     47,      8,      0,     1;
04 :    394,     94,     12,     0,    1;
05 :   2082,   1608,    282,    32,    0,    2;
06 :  15113,   8812,   3452,   512,   58,    0,   3;
07 : 111664,  73863,  22310,  5962,  790,   96,   0,  4;
08 : 789930, 631700, 218608, 45762, 9374, 1260, 142,  0,  5;
		

Links

• Alois P. Heinz, Rows n = 0..140, flattened
• Wikipedia, Pentomino

Crossrefs

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

Column k=0 gives A247767.

Main diagonal gives A003520.

Cf. A247736.