A247713 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape Z; triangle T(n,k), n>=0, read by rows.

1, 1, 5, 52, 4, 451, 48, 2, 3498, 484, 24, 23502, 4136, 300, 12, 173611, 37674, 3262, 142, 1323447, 335388, 35938, 1964, 44, 9920654, 2892492, 365458, 25752, 986, 12, 73573634, 24266128, 3544842, 298200, 15002, 400, 6, 545170514, 200531918, 33123244, 3236018, 198380, 7546, 164, 2

Offset

0,3

Comments

Sum_{k>0} k * T(n,k) = A247746(n).

Links

Alois P. Heinz, Rows n = 0..170, flattened

Wikipedia, Pentomino

Example

T(3,1) = 4:
._____.        ._____.
|___. |        |   ._|
|_. | |        |___| |
| | |_|        | .___|
| |___|        |_|   |
|_____| (*2)   |_____| (*2)  .
Triangle T(n,k) begins:
00 :        1;
01 :        1;
02 :        5;
03 :       52,        4;
04 :      451,       48,       2;
05 :     3498,      484,      24;
06 :    23502,     4136,     300,     12;
07 :   173611,    37674,    3262,    142;
08 :  1323447,   335388,   35938,   1964,    44;
09 :  9920654,  2892492,  365458,  25752,   986,  12;
10 : 73573634, 24266128, 3544842, 298200, 15002, 400, 6;

Crossrefs

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

Column k=0 gives A247777.

Cf. A247746.

Sequence in context: A134097 A299025 A247702 * A067282 A045539 A281202

Adjacent sequences: A247710 A247711 A247712 * A247714 A247715 A247716

Keyword

nonn,tabf

Author

Alois P. Heinz, Sep 23 2014

Status

approved