A247702 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape F; triangle T(n,k), n>=0, 0<=k<=max(delta_{3,n},floor((n-2)/2)*2), read by rows.

1, 1, 5, 52, 4, 437, 60, 4, 3342, 584, 80, 21734, 5372, 818, 24, 2, 155685, 49540, 8800, 620, 44, 1153475, 439780, 92500, 10140, 856, 28, 2, 8422634, 3726836, 914142, 127596, 13338, 760, 48, 60853524, 30683256, 8544440, 1425320, 176156, 14404, 1078, 32, 2

Offset

0,3

Comments

Sum_{k>0} k * T(n,k) = A247735(n).

Links

Alois P. Heinz, Rows n = 0..150, flattened

Wikipedia, Pentomino

Example

T(3,1) = 4:
._____.  ._____.  ._____.  ._____.
|_.   |  |   ._|  | ._. |  | ._. |
| |___|  |___| |  |_| |_|  |_| |_|
|_. ._|  |_. ._|  | .___|  |___. |
| |_| |  | |_| |  |_|   |  |   |_|
|_____|  |_____|  |_____|  |_____| .
Triangle T(n,k) begins:
00 :        1;
01 :        1;
02 :        5;
03 :       52,        4;
04 :      437,       60,       4;
05 :     3342,      584,      80;
06 :    21734,     5372,     818,      24,      2;
07 :   155685,    49540,    8800,     620,     44;
08 :  1153475,   439780,   92500,   10140,    856,    28,    2;
09 :  8422634,  3726836,  914142,  127596,  13338,   760,   48;
10 : 60853524, 30683256, 8544440, 1425320, 176156, 14404, 1078, 32, 2;

Crossrefs

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

Column k=0 gives A247766.

Cf. A247735.

Sequence in context: A022501 A134097 A299025 * A247713 A067282 A045539

Adjacent sequences: A247699 A247700 A247701 * A247703 A247704 A247705

Keyword

nonn,tabf

Author

Alois P. Heinz, Sep 22 2014

Status

approved