A247704 - OEIS

%I #14 Feb 07 2017 10:14:07

%S 1,1,0,3,0,2,36,16,4,0,177,220,100,0,4,1300,1720,816,144,26,0,8866,

%T 11152,5616,1784,524,0,8,54849,85016,51116,18380,4656,584,88,0,372943,

%U 622732,448744,189360,52130,8948,1908,0,16,2466986,4528336,3670116,1806160,582250,127140,22206,1912,248,0

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

%C Sum_{k>0} k * T(n,k) = A247737(n).

%H Alois P. Heinz, <a href="/A247704/b247704.txt">Rows n = 0..140, flattened</a>

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

%e T(2,2) = 2:

%e .___.   .___.

%e | ._|   |_. |

%e | | |   | | |

%e | | |   | | |

%e |_| |   | |_|

%e |___|   |___| .

%e Triangle T(n,k) begins:

%e 00 :      1;

%e 01 :      1,      0;

%e 02 :      3,      0,      2;

%e 03 :     36,     16,      4,      0;

%e 04 :    177,    220,    100,      0,     4;

%e 05 :   1300,   1720,    816,    144,    26,    0;

%e 06 :   8866,  11152,   5616,   1784,   524,    0,    8;

%e 07 :  54849,  85016,  51116,  18380,  4656,  584,   88,  0;

%e 08 : 372943, 622732, 448744, 189360, 52130, 8948, 1908,  0, 16;

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

%Y Column k=0 gives A247768.

%Y Cf. A247737.

%K nonn,tabl

%O 0,4

%A _Alois P. Heinz_, Sep 22 2014