A247711 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape X; triangle T(n,k), n>=0, read by rows.

1, 1, 5, 55, 1, 493, 8, 3930, 76, 27207, 734, 9, 207118, 7414, 157, 1622723, 71986, 2064, 8, 12544364, 638499, 22232, 259, 95912510, 5558790, 222964, 3898, 50, 732066083, 47971603, 2179607, 49537, 948, 8, 5616480627, 410502410, 20604626, 564498, 13889, 180

Offset

0,3

Comments

Sum_{k>0} k * T(n,k) = A247744(n).

Links

Alois P. Heinz, Rows n = 0..185, flattened

Wikipedia, Pentomino

Example

T(3,1) = 1:
._____.
| ._. |
|_| |_|
|_. ._|
| |_| |
|_____|
.
Triangle T(n,k) begins:
00 :        1;
01 :        1;
02 :        5;
03 :       55,       1;
04 :      493,       8;
05 :     3930,      76;
06 :    27207,     734,      9;
07 :   207118,    7414,    157;
08 :  1622723,   71986,   2064,    8;
09 : 12544364,  638499,  22232,  259;
10 : 95912510, 5558790, 222964, 3898, 50;

Crossrefs

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

Columns k=0-1 give: A247775, A247828.

Cf. A247744.

Sequence in context: A245765 A085719 A129420 * A284066 A244439 A216446

Adjacent sequences: A247708 A247709 A247710 * A247712 A247713 A247714

Keyword

nonn,tabf

Author

Alois P. Heinz, Sep 23 2014

Status

approved