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A247708 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape U; triangle T(n,k), n>=0, read by rows. 5
1, 1, 5, 39, 16, 1, 369, 120, 12, 2908, 1000, 98, 19185, 7474, 1228, 60, 3, 137200, 63896, 12448, 1092, 53, 1022915, 540562, 120034, 12676, 590, 4, 7606043, 4365686, 1084022, 140512, 8836, 250, 5, 55699672, 34738058, 9663366, 1466724, 124242, 5984, 166 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Sum_{k>0} k * T(n,k) = A247741(n).
LINKS
Wikipedia, Pentomino
EXAMPLE
T(3,2) = 1:
._____.
| ._. |
|_| |_|
|_. ._|
| |_| |
|_____| .
Triangle T(n,k) begins:
00 : 1;
01 : 1;
02 : 5;
03 : 39, 16, 1;
04 : 369, 120, 12;
05 : 2908, 1000, 98;
06 : 19185, 7474, 1228, 60, 3;
07 : 137200, 63896, 12448, 1092, 53;
08 : 1022915, 540562, 120034, 12676, 590, 4;
09 : 7606043, 4365686, 1084022, 140512, 8836, 250, 5;
10 : 55699672, 34738058, 9663366, 1466724, 124242, 5984, 166;
CROSSREFS
Row sums give A174249 or A233427(n,5).
Column k=0 gives A247772.
Cf. A247741.
Sequence in context: A221845 A299054 A095230 * A171555 A153267 A183477
KEYWORD
nonn,tabf
AUTHOR
Alois P. Heinz, Sep 22 2014
STATUS
approved

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Last modified April 25 10:22 EDT 2024. Contains 371967 sequences. (Running on oeis4.)