A247705 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape N; triangle T(n,k), n>=0, read by rows.

1, 1, 5, 48, 8, 423, 68, 10, 3082, 832, 84, 8, 18998, 7624, 1230, 88, 10, 133083, 65360, 14390, 1732, 116, 8, 965175, 555236, 150876, 23184, 2196, 108, 6, 6907447, 4531744, 1454292, 275320, 33807, 2616, 124, 4, 48357538, 36466396, 13354738, 3012116, 457360, 46872, 3086, 104, 2

Offset

0,3

Comments

Sum_{k>0} k * T(n,k) = A247738(n).

Links

Alois P. Heinz, Rows n = 0..160, flattened

Wikipedia, Pentomino

Example

T(3,1) = 8:
._____.        .___._.
| ._. |        | ._| |
|_| |_|        | | ._|
| ._| |        | | | |
| |   |        |_|_| |
|_|___| (*4)   |_____| (*4)  .
Triangle T(n,k) begins:
00 :      1;
01 :      1;
02 :      5;
03 :     48,      8;
04 :    423,     68,     10;
05 :   3082,    832,     84,     8;
06 :  18998,   7624,   1230,    88,   10;
07 : 133083,  65360,  14390,  1732,  116,   8;
08 : 965175, 555236, 150876, 23184, 2196, 108,  6;

Crossrefs

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

Column k=0 gives A247769.

Cf. A247738.

Sequence in context: A086776 A259502 A291863 * A215543 A212111 A359969

Adjacent sequences: A247702 A247703 A247704 * A247706 A247707 A247708

Keyword

nonn,tabf

Author

Alois P. Heinz, Sep 22 2014

Status

approved