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A247709
Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape V; triangle T(n,k), n>=0, 0<=k<=max(0,n-2+delta_{n,3}), read by rows.
5
1, 1, 5, 38, 16, 2, 329, 152, 20, 2614, 1224, 160, 8, 17400, 8656, 1714, 168, 12, 122843, 72104, 17280, 2300, 158, 4, 901647, 598444, 168422, 25872, 2284, 108, 4, 6662758, 4770520, 1479850, 260672, 29166, 2256, 124, 8, 48492622, 37416964, 12800398, 2601524, 351578, 32840, 2182, 100, 4
OFFSET
0,3
COMMENTS
Sum_{k>0} k * T(n,k) = A247742(n).
LINKS
Wikipedia, Pentomino
EXAMPLE
T(3,2) = 2:
._____. ._____.
| .___| |___. |
| | ._| |_. | |
|_| | | | | |_|
|___| | | |___|
|_____| |_____| .
Triangle T(n,k) begins:
00 : 1;
01 : 1;
02 : 5;
03 : 38, 16, 2;
04 : 329, 152, 20;
05 : 2614, 1224, 160, 8;
06 : 17400, 8656, 1714, 168, 12;
07 : 122843, 72104, 17280, 2300, 158, 4;
08 : 901647, 598444, 168422, 25872, 2284, 108, 4;
09 : 6662758, 4770520, 1479850, 260672, 29166, 2256, 124, 8;
10 : 48492622, 37416964, 12800398, 2601524, 351578, 32840, 2182, 100, 4;
CROSSREFS
Row sums give A174249 or A233427(n,5).
Column k=0 gives A247773.
Cf. A247742.
Sequence in context: A086877 A372839 A061674 * A097276 A280437 A222646
KEYWORD
nonn,tabf
AUTHOR
Alois P. Heinz, Sep 22 2014
STATUS
approved