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A247706
Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape P; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
6
1, 1, 0, 3, 0, 2, 16, 20, 20, 0, 135, 204, 140, 16, 6, 944, 1432, 1164, 296, 170, 0, 4814, 8796, 8452, 4068, 1708, 92, 20, 26435, 58656, 66994, 41648, 17494, 2700, 762, 0, 158761, 410000, 520728, 371456, 175810, 46648, 12876, 440, 62, 978044, 2783560, 3836254, 3107308, 1696312, 609772, 172724, 18220, 3160, 0
OFFSET
0,4
COMMENTS
Sum_{k>0} k * T(n,k) = A247739(n).
LINKS
Wikipedia, Pentomino
EXAMPLE
T(2,2) = 2:
.___. .___.
| | | |
| ._| |_. |
|_| | | |_|
| | | |
|___| |___| .
Triangle T(n,k) begins:
00 : 1;
01 : 1, 0;
02 : 3, 0, 2;
03 : 16, 20, 20, 0;
04 : 135, 204, 140, 16, 6;
05 : 944, 1432, 1164, 296, 170, 0;
06 : 4814, 8796, 8452, 4068, 1708, 92, 20;
07 : 26435, 58656, 66994, 41648, 17494, 2700, 762, 0;
08 : 158761, 410000, 520728, 371456, 175810, 46648, 12876, 440, 62;
CROSSREFS
Row sums give A174249 or A233427(n,5).
Column k=0 gives A247770.
Even bisection of main diagonal gives A247076.
Cf. A247739.
Sequence in context: A303102 A302953 A350464 * A361527 A247704 A372344
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Sep 22 2014
STATUS
approved