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.

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

Alois P. Heinz, Rows n = 0..175, flattened

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

Adjacent sequences: A247704 A247705 A247706 * A247708 A247709 A247710

Keyword

nonn,tabf

Author

Alois P. Heinz, Sep 22 2014

Status

approved