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A247705
Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape N; triangle T(n,k), n>=0, read by rows.
5
1, 1, 5, 48, 8, 423, 68, 10, 3082, 832, 84, 8, 18998, 7624, 1230, 88, 10, 133083, 65360, 14390, 1732, 116, 8, 965175, 555236, 150876, 23184, 2196, 108, 6, 6907447, 4531744, 1454292, 275320, 33807, 2616, 124, 4, 48357538, 36466396, 13354738, 3012116, 457360, 46872, 3086, 104, 2
OFFSET
0,3
COMMENTS
Sum_{k>0} k * T(n,k) = A247738(n).
LINKS
Wikipedia, Pentomino
EXAMPLE
T(3,1) = 8:
._____. .___._.
| ._. | | ._| |
|_| |_| | | ._|
| ._| | | | | |
| | | |_|_| |
|_|___| (*4) |_____| (*4) .
Triangle T(n,k) begins:
00 : 1;
01 : 1;
02 : 5;
03 : 48, 8;
04 : 423, 68, 10;
05 : 3082, 832, 84, 8;
06 : 18998, 7624, 1230, 88, 10;
07 : 133083, 65360, 14390, 1732, 116, 8;
08 : 965175, 555236, 150876, 23184, 2196, 108, 6;
CROSSREFS
Row sums give A174249 or A233427(n,5).
Column k=0 gives A247769.
Cf. A247738.
Sequence in context: A086776 A259502 A291863 * A215543 A212111 A359969
KEYWORD
nonn,tabf
AUTHOR
Alois P. Heinz, Sep 22 2014
STATUS
approved