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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. 6
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 (list; table; graph; refs; listen; history; text; internal format)
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: A302381 A303102 A302953 * A247704 A127802 A165951

Adjacent sequences:  A247703 A247704 A247705 * A247707 A247708 A247709

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Sep 22 2014

STATUS

approved

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Last modified December 14 12:04 EST 2019. Contains 329979 sequences. (Running on oeis4.)