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A247712
Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape Y; triangle T(n,k), n>=0, read by rows.
5
1, 1, 5, 44, 12, 321, 136, 44, 2404, 1160, 404, 24, 14, 14692, 9380, 3388, 392, 90, 8, 98831, 78492, 30834, 5724, 748, 60, 684729, 631020, 292250, 74016, 13280, 1428, 58, 4642752, 4944856, 2628566, 788284, 171368, 25648, 3648, 228, 4
OFFSET
0,3
COMMENTS
Sum_{k>0} k * T(n,k) = A247745(n).
T(10*n,10*n) = 10^n = A011557(n).
LINKS
Wikipedia, Pentomino
EXAMPLE
T(3,1) = 12:
._____. ._____. ._____.
| |_. | |_. | | |_. |
| ._| | | |___| | ._| |
| | | | | ._| | | |___|
|_| |_| | | | |_| |
|_____| (*4) |_|___| (*4) |_____| (*4) .
T(10,10) = 10:
.___________________.
|_. .___| |___. ._| |
| |_| |_______|_|_. |
| |_______|___. ._| |
| ._| |___. ._|_| |_|
|_|_______|_|_______| ... .
Triangle T(n,k) begins:
00 : 1;
01 : 1;
02 : 5;
03 : 44, 12;
04 : 321, 136, 44;
05 : 2404, 1160, 404, 24, 14;
06 : 14692, 9380, 3388, 392, 90, 8;
07 : 98831, 78492, 30834, 5724, 748, 60;
08 : 684729, 631020, 292250, 74016, 13280, 1428, 58;
CROSSREFS
Row sums give A174249 or A233427(n,5).
Column k=0 gives A247776.
Sequence in context: A142726 A079646 A292697 * A030698 A080284 A193458
KEYWORD
nonn,tabf
AUTHOR
Alois P. Heinz, Sep 23 2014
STATUS
approved