A247707 - OEIS

%I #15 Feb 06 2017 19:04:05

%S 1,1,5,50,6,437,62,2,3270,700,36,21720,5712,506,12,160593,48364,5444,

%T 282,6,1209537,425638,57648,3836,122,8999307,3578302,576791,48688,

%U 2226,40,66054288,29550476,5500946,558036,33400,1056,10,485082083,239927980,50762537,6035146,440480,19180,380

%N Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape T; triangle T(n,k), n>=0, 0<=k<=max(0,floor(2*(n-1)/3)), read by rows.

%C Sum_{k>0} k * T(n,k) = A247740(n).

%H Alois P. Heinz, <a href="/A247707/b247707.txt">Rows n = 0..175, flattened</a>

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

%e T(4,2) = 2:

%e ._____._.    ._._____.

%e |_. ._| |    | |_. ._|

%e | | |_. |    | ._| | |

%e | |_| | |    | | |_| |

%e | ._| |_|    |_| |_. |

%e |_|_____|    |_____|_| .

%e Triangle T(n,k) begins:

%e 00 :        1;

%e 01 :        1;

%e 02 :        5;

%e 03 :       50,        6;

%e 04 :      437,       62,       2;

%e 05 :     3270,      700,      36;

%e 06 :    21720,     5712,     506,     12;

%e 07 :   160593,    48364,    5444,    282,     6;

%e 08 :  1209537,   425638,   57648,   3836,   122;

%e 09 :  8999307,  3578302,  576791,  48688,  2226,   40;

%e 10 : 66054288, 29550476, 5500946, 558036, 33400, 1056, 10;

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

%Y Column k=0 gives A247771.

%Y Cf. A247740.

%K nonn,tabf

%O 0,3

%A _Alois P. Heinz_, Sep 22 2014