A247712 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape Y; triangle T(n,k), n>=0, read by rows.

1, 1, 5, 44, 12, 321, 136, 44, 2404, 1160, 404, 24, 14, 14692, 9380, 3388, 392, 90, 8, 98831, 78492, 30834, 5724, 748, 60, 684729, 631020, 292250, 74016, 13280, 1428, 58, 4642752, 4944856, 2628566, 788284, 171368, 25648, 3648, 228, 4

Offset

0,3

Comments

Sum_{k>0} k * T(n,k) = A247745(n).

T(10*n,10*n) = 10^n = A011557(n).

Links

Alois P. Heinz, Rows n = 0..145, flattened

Wikipedia, Pentomino

Example

T(3,1) = 12:
._____.        ._____.        ._____.
| |_. |        |_.   |        | |_. |
| ._| |        | |___|        | ._| |
| | | |        | ._| |        | |___|
|_| |_|        | |   |        |_|   |
|_____| (*4)   |_|___| (*4)   |_____| (*4)  .
T(10,10) = 10:
.___________________.
|_. .___| |___. ._| |
| |_| |_______|_|_. |
| |_______|___. ._| |
| ._| |___. ._|_| |_|
|_|_______|_|_______| ... .
Triangle T(n,k) begins:
00 :      1;
01 :      1;
02 :      5;
03 :     44,     12;
04 :    321,    136,     44;
05 :   2404,   1160,    404,    24,    14;
06 :  14692,   9380,   3388,   392,    90,    8;
07 :  98831,  78492,  30834,  5724,   748,   60;
08 : 684729, 631020, 292250, 74016, 13280, 1428, 58;

Crossrefs

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

Column k=0 gives A247776.

Cf. A011557, A247745.

Sequence in context: A142726 A079646 A292697 * A030698 A080284 A193458

Adjacent sequences: A247709 A247710 A247711 * A247713 A247714 A247715

Keyword

nonn,tabf

Author

Alois P. Heinz, Sep 23 2014

Status

approved