A247704 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape L; triangle T(n,k), n>=0, 0<=k<=n, read by rows.

1, 1, 0, 3, 0, 2, 36, 16, 4, 0, 177, 220, 100, 0, 4, 1300, 1720, 816, 144, 26, 0, 8866, 11152, 5616, 1784, 524, 0, 8, 54849, 85016, 51116, 18380, 4656, 584, 88, 0, 372943, 622732, 448744, 189360, 52130, 8948, 1908, 0, 16, 2466986, 4528336, 3670116, 1806160, 582250, 127140, 22206, 1912, 248, 0

Offset

0,4

Comments

Sum_{k>0} k * T(n,k) = A247737(n).

Links

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

Wikipedia, Pentomino

Example

T(2,2) = 2:
.___.   .___.
| ._|   |_. |
| | |   | | |
| | |   | | |
|_| |   | |_|
|___|   |___| .
Triangle T(n,k) begins:
00 :      1;
01 :      1,      0;
02 :      3,      0,      2;
03 :     36,     16,      4,      0;
04 :    177,    220,    100,      0,     4;
05 :   1300,   1720,    816,    144,    26,    0;
06 :   8866,  11152,   5616,   1784,   524,    0,    8;
07 :  54849,  85016,  51116,  18380,  4656,  584,   88,  0;
08 : 372943, 622732, 448744, 189360, 52130, 8948, 1908,  0, 16;

Crossrefs

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

Column k=0 gives A247768.

Cf. A247737.

Sequence in context: A350464 A247706 A361527 * A372344 A127802 A165951

Adjacent sequences: A247701 A247702 A247703 * A247705 A247706 A247707

Keyword

nonn,tabl

Author

Alois P. Heinz, Sep 22 2014

Status

approved