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A247708 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape U; triangle T(n,k), n>=0, read by rows. 5
1, 1, 5, 39, 16, 1, 369, 120, 12, 2908, 1000, 98, 19185, 7474, 1228, 60, 3, 137200, 63896, 12448, 1092, 53, 1022915, 540562, 120034, 12676, 590, 4, 7606043, 4365686, 1084022, 140512, 8836, 250, 5, 55699672, 34738058, 9663366, 1466724, 124242, 5984, 166 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Sum_{k>0} k * T(n,k) = A247741(n).

LINKS

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

Wikipedia, Pentomino

EXAMPLE

T(3,2) = 1:

._____.

| ._. |

|_| |_|

|_. ._|

| |_| |

|_____| .

Triangle T(n,k) begins:

00 :        1;

01 :        1;

02 :        5;

03 :       39,       16,       1;

04 :      369,      120,      12;

05 :     2908,     1000,      98;

06 :    19185,     7474,    1228,      60,      3;

07 :   137200,    63896,   12448,    1092,     53;

08 :  1022915,   540562,  120034,   12676,    590,    4;

09 :  7606043,  4365686, 1084022,  140512,   8836,  250,   5;

10 : 55699672, 34738058, 9663366, 1466724, 124242, 5984, 166;

CROSSREFS

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

Column k=0 gives A247772.

Cf. A247741.

Sequence in context: A221845 A299054 A095230 * A171555 A153267 A183477

Adjacent sequences:  A247705 A247706 A247707 * A247709 A247710 A247711

KEYWORD

nonn,tabf

AUTHOR

Alois P. Heinz, Sep 22 2014

STATUS

approved

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Last modified October 28 17:39 EDT 2021. Contains 348329 sequences. (Running on oeis4.)