A247711 - OEIS

A247711

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

%I #17 May 09 2018 10:00:13

%S 1,1,5,55,1,493,8,3930,76,27207,734,9,207118,7414,157,1622723,71986,

%T 2064,8,12544364,638499,22232,259,95912510,5558790,222964,3898,50,

%U 732066083,47971603,2179607,49537,948,8,5616480627,410502410,20604626,564498,13889,180

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

%C Sum_{k>0} k * T(n,k) = A247744(n).

%H Alois P. Heinz, <a href="/A247711/b247711.txt">Rows n = 0..185, flattened</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>

%e T(3,1) = 1:

%e ._____.

%e | ._. |

%e |_| |_|

%e |_. ._|

%e | |_| |

%e |_____|

%e .

%e Triangle T(n,k) begins:

%e 00 : 1;

%e 01 : 1;

%e 02 : 5;

%e 03 : 55, 1;

%e 04 : 493, 8;

%e 05 : 3930, 76;

%e 06 : 27207, 734, 9;

%e 07 : 207118, 7414, 157;

%e 08 : 1622723, 71986, 2064, 8;

%e 09 : 12544364, 638499, 22232, 259;

%e 10 : 95912510, 5558790, 222964, 3898, 50;

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

%Y Columns k=0-1 give: A247775, A247828.

%Y Cf. A247744.

%K nonn,tabf

%O 0,3

%A _Alois P. Heinz_, Sep 23 2014