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A247713
Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape Z; triangle T(n,k), n>=0, read by rows.
5
1, 1, 5, 52, 4, 451, 48, 2, 3498, 484, 24, 23502, 4136, 300, 12, 173611, 37674, 3262, 142, 1323447, 335388, 35938, 1964, 44, 9920654, 2892492, 365458, 25752, 986, 12, 73573634, 24266128, 3544842, 298200, 15002, 400, 6, 545170514, 200531918, 33123244, 3236018, 198380, 7546, 164, 2
OFFSET
0,3
COMMENTS
Sum_{k>0} k * T(n,k) = A247746(n).
LINKS
Wikipedia, Pentomino
EXAMPLE
T(3,1) = 4:
._____. ._____.
|___. | | ._|
|_. | | |___| |
| | |_| | .___|
| |___| |_| |
|_____| (*2) |_____| (*2) .
Triangle T(n,k) begins:
00 : 1;
01 : 1;
02 : 5;
03 : 52, 4;
04 : 451, 48, 2;
05 : 3498, 484, 24;
06 : 23502, 4136, 300, 12;
07 : 173611, 37674, 3262, 142;
08 : 1323447, 335388, 35938, 1964, 44;
09 : 9920654, 2892492, 365458, 25752, 986, 12;
10 : 73573634, 24266128, 3544842, 298200, 15002, 400, 6;
CROSSREFS
Row sums give A174249 or A233427(n,5).
Column k=0 gives A247777.
Cf. A247746.
Sequence in context: A134097 A299025 A247702 * A067282 A045539 A281202
KEYWORD
nonn,tabf
AUTHOR
Alois P. Heinz, Sep 23 2014
STATUS
approved