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

0,4

Comments

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

Links

Alois P. Heinz, Rows n = 0..140, flattened

Wikipedia, Pentomino

Example

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;

Crossrefs

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

Column k=0 gives A247767.

Main diagonal gives A003520.

Cf. A247736.

Sequence in context: A342202 A355997 A136452 * A280639 A350708 A319037

Adjacent sequences: A247700 A247701 A247702 * A247704 A247705 A247706

Keyword

nonn,tabl

Author

Alois P. Heinz, Sep 22 2014

Status

approved