A247706 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape P; triangle T(n,k), n>=0, 0<=k<=n, read by rows.

1, 1, 0, 3, 0, 2, 16, 20, 20, 0, 135, 204, 140, 16, 6, 944, 1432, 1164, 296, 170, 0, 4814, 8796, 8452, 4068, 1708, 92, 20, 26435, 58656, 66994, 41648, 17494, 2700, 762, 0, 158761, 410000, 520728, 371456, 175810, 46648, 12876, 440, 62, 978044, 2783560, 3836254, 3107308, 1696312, 609772, 172724, 18220, 3160, 0

Offset

0,4

Comments

Sum_{k>0} k * T(n,k) = A247739(n).

Links

Alois P. Heinz, Rows n = 0..140, flattened

Wikipedia, Pentomino

Example

T(2,2) = 2:
.___.   .___.
|   |   |   |
| ._|   |_. |
|_| |   | |_|
|   |   |   |
|___|   |___| .
Triangle T(n,k) begins:
00 :      1;
01 :      1,      0;
02 :      3,      0,      2;
03 :     16,     20,     20,      0;
04 :    135,    204,    140,     16,      6;
05 :    944,   1432,   1164,    296,    170,     0;
06 :   4814,   8796,   8452,   4068,   1708,    92,    20;
07 :  26435,  58656,  66994,  41648,  17494,  2700,   762,   0;
08 : 158761, 410000, 520728, 371456, 175810, 46648, 12876, 440, 62;

Crossrefs

Row sums give A174249 or A233427(n,5).

Column k=0 gives A247770.

Even bisection of main diagonal gives A247076.

Cf. A247739.

Sequence in context: A303102 A302953 A350464 * A361527 A247704 A372344

Adjacent sequences: A247703 A247704 A247705 * A247707 A247708 A247709

Keyword

nonn,tabl

Author

Alois P. Heinz, Sep 22 2014

Status

approved