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A247707
Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape T; triangle T(n,k), n>=0, 0<=k<=max(0,floor(2*(n-1)/3)), read by rows.
5
1, 1, 5, 50, 6, 437, 62, 2, 3270, 700, 36, 21720, 5712, 506, 12, 160593, 48364, 5444, 282, 6, 1209537, 425638, 57648, 3836, 122, 8999307, 3578302, 576791, 48688, 2226, 40, 66054288, 29550476, 5500946, 558036, 33400, 1056, 10, 485082083, 239927980, 50762537, 6035146, 440480, 19180, 380
OFFSET
0,3
COMMENTS
Sum_{k>0} k * T(n,k) = A247740(n).
LINKS
Wikipedia, Pentomino
EXAMPLE
T(4,2) = 2:
._____._. ._._____.
|_. ._| | | |_. ._|
| | |_. | | ._| | |
| |_| | | | | |_| |
| ._| |_| |_| |_. |
|_|_____| |_____|_| .
Triangle T(n,k) begins:
00 : 1;
01 : 1;
02 : 5;
03 : 50, 6;
04 : 437, 62, 2;
05 : 3270, 700, 36;
06 : 21720, 5712, 506, 12;
07 : 160593, 48364, 5444, 282, 6;
08 : 1209537, 425638, 57648, 3836, 122;
09 : 8999307, 3578302, 576791, 48688, 2226, 40;
10 : 66054288, 29550476, 5500946, 558036, 33400, 1056, 10;
CROSSREFS
Row sums give A174249 or A233427(n,5).
Column k=0 gives A247771.
Cf. A247740.
Sequence in context: A084765 A203411 A218322 * A082795 A217398 A059008
KEYWORD
nonn,tabf
AUTHOR
Alois P. Heinz, Sep 22 2014
STATUS
approved