A247708 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape U; triangle T(n,k), n>=0, read by rows.

1, 1, 5, 39, 16, 1, 369, 120, 12, 2908, 1000, 98, 19185, 7474, 1228, 60, 3, 137200, 63896, 12448, 1092, 53, 1022915, 540562, 120034, 12676, 590, 4, 7606043, 4365686, 1084022, 140512, 8836, 250, 5, 55699672, 34738058, 9663366, 1466724, 124242, 5984, 166

Offset

0,3

Comments

Sum_{k>0} k * T(n,k) = A247741(n).

Links

Alois P. Heinz, Rows n = 0..175, flattened

Wikipedia, Pentomino

Example

T(3,2) = 1:
._____.
| ._. |
|_| |_|
|_. ._|
| |_| |
|_____| .
Triangle T(n,k) begins:
00 :        1;
01 :        1;
02 :        5;
03 :       39,       16,       1;
04 :      369,      120,      12;
05 :     2908,     1000,      98;
06 :    19185,     7474,    1228,      60,      3;
07 :   137200,    63896,   12448,    1092,     53;
08 :  1022915,   540562,  120034,   12676,    590,    4;
09 :  7606043,  4365686, 1084022,  140512,   8836,  250,   5;
10 : 55699672, 34738058, 9663366, 1466724, 124242, 5984, 166;

Crossrefs

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

Column k=0 gives A247772.

Cf. A247741.

Sequence in context: A221845 A299054 A095230 * A171555 A153267 A183477

Adjacent sequences: A247705 A247706 A247707 * A247709 A247710 A247711

Keyword

nonn,tabf

Author

Alois P. Heinz, Sep 22 2014

Status

approved