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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.
5
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
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
KEYWORD
nonn,tabf
AUTHOR
Alois P. Heinz, Sep 22 2014
STATUS
approved