cp's OEIS Frontend

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.

%I A247708 #12 Feb 06 2017 19:02:32
%S A247708 1,1,5,39,16,1,369,120,12,2908,1000,98,19185,7474,1228,60,3,137200,
%T A247708 63896,12448,1092,53,1022915,540562,120034,12676,590,4,7606043,
%U A247708 4365686,1084022,140512,8836,250,5,55699672,34738058,9663366,1466724,124242,5984,166
%N 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.
%C A247708 Sum_{k>0} k * T(n,k) = A247741(n).
%H A247708 Alois P. Heinz, <a href="/A247708/b247708.txt">Rows n = 0..175, flattened</a>
%H A247708 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%e A247708 T(3,2) = 1:
%e A247708 ._____.
%e A247708 | ._. |
%e A247708 |_| |_|
%e A247708 |_. ._|
%e A247708 | |_| |
%e A247708 |_____| .
%e A247708 Triangle T(n,k) begins:
%e A247708 00 :        1;
%e A247708 01 :        1;
%e A247708 02 :        5;
%e A247708 03 :       39,       16,       1;
%e A247708 04 :      369,      120,      12;
%e A247708 05 :     2908,     1000,      98;
%e A247708 06 :    19185,     7474,    1228,      60,      3;
%e A247708 07 :   137200,    63896,   12448,    1092,     53;
%e A247708 08 :  1022915,   540562,  120034,   12676,    590,    4;
%e A247708 09 :  7606043,  4365686, 1084022,  140512,   8836,  250,   5;
%e A247708 10 : 55699672, 34738058, 9663366, 1466724, 124242, 5984, 166;
%Y A247708 Row sums give A174249 or A233427(n,5).
%Y A247708 Column k=0 gives A247772.
%Y A247708 Cf. A247741.
%K A247708 nonn,tabf
%O A247708 0,3
%A A247708 _Alois P. Heinz_, Sep 22 2014