A247709 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape V; triangle T(n,k), n>=0, 0<=k<=max(0,n-2+delta_{n,3}), read by rows.

1, 1, 5, 38, 16, 2, 329, 152, 20, 2614, 1224, 160, 8, 17400, 8656, 1714, 168, 12, 122843, 72104, 17280, 2300, 158, 4, 901647, 598444, 168422, 25872, 2284, 108, 4, 6662758, 4770520, 1479850, 260672, 29166, 2256, 124, 8, 48492622, 37416964, 12800398, 2601524, 351578, 32840, 2182, 100, 4

Offset

0,3

Comments

Sum_{k>0} k * T(n,k) = A247742(n).

Links

Alois P. Heinz, Rows n = 0..145, flattened

Wikipedia, Pentomino

Example

T(3,2) = 2:
._____.    ._____.
| .___|    |___. |
| | ._|    |_. | |
|_| | |    | | |_|
|___| |    | |___|
|_____|    |_____| .
Triangle T(n,k) begins:
00 :        1;
01 :        1;
02 :        5;
03 :       38,       16,        2;
04 :      329,      152,       20;
05 :     2614,     1224,      160,       8;
06 :    17400,     8656,     1714,     168,     12;
07 :   122843,    72104,    17280,    2300,    158,     4;
08 :   901647,   598444,   168422,   25872,   2284,   108,    4;
09 :  6662758,  4770520,  1479850,  260672,  29166,  2256,  124,   8;
10 : 48492622, 37416964, 12800398, 2601524, 351578, 32840, 2182, 100, 4;

Crossrefs

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

Column k=0 gives A247773.

Cf. A247742.

Sequence in context: A350966 A086877 A061674 * A097276 A280437 A222646

Adjacent sequences: A247706 A247707 A247708 * A247710 A247711 A247712

Keyword

nonn,tabf

Author

Alois P. Heinz, Sep 22 2014

Status

approved