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A247703
Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape I; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
5
1, 0, 1, 4, 0, 1, 47, 8, 0, 1, 394, 94, 12, 0, 1, 2082, 1608, 282, 32, 0, 2, 15113, 8812, 3452, 512, 58, 0, 3, 111664, 73863, 22310, 5962, 790, 96, 0, 4, 789930, 631700, 218608, 45762, 9374, 1260, 142, 0, 5, 5388729, 5157928, 2067811, 491868, 81720, 15272, 1824, 196, 0, 6
OFFSET
0,4
COMMENTS
Sum_{k>0} k * T(n,k) = A247736(n).
LINKS
Wikipedia, Pentomino
EXAMPLE
T(5,5) = 2:
._._._._._. ._________.
| | | | | | |_________|
| | | | | | |_________|
| | | | | | |_________|
| | | | | | |_________|
|_|_|_|_|_| |_________| .
Triangle T(n,k) begins:
00 : 1;
01 : 0, 1;
02 : 4, 0, 1;
03 : 47, 8, 0, 1;
04 : 394, 94, 12, 0, 1;
05 : 2082, 1608, 282, 32, 0, 2;
06 : 15113, 8812, 3452, 512, 58, 0, 3;
07 : 111664, 73863, 22310, 5962, 790, 96, 0, 4;
08 : 789930, 631700, 218608, 45762, 9374, 1260, 142, 0, 5;
CROSSREFS
Row sums give A174249 or A233427(n,5).
Column k=0 gives A247767.
Main diagonal gives A003520.
Cf. A247736.
Sequence in context: A342202 A355997 A136452 * A280639 A350708 A319037
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Sep 22 2014
STATUS
approved