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%I #18 Feb 06 2017 18:33:46
%S 1,1,0,3,0,2,16,20,20,0,135,204,140,16,6,944,1432,1164,296,170,0,4814,
%T 8796,8452,4068,1708,92,20,26435,58656,66994,41648,17494,2700,762,0,
%U 158761,410000,520728,371456,175810,46648,12876,440,62,978044,2783560,3836254,3107308,1696312,609772,172724,18220,3160,0
%N Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape P; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
%C Sum_{k>0} k * T(n,k) = A247739(n).
%H Alois P. Heinz, <a href="/A247706/b247706.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 : 16, 20, 20, 0;
%e 04 : 135, 204, 140, 16, 6;
%e 05 : 944, 1432, 1164, 296, 170, 0;
%e 06 : 4814, 8796, 8452, 4068, 1708, 92, 20;
%e 07 : 26435, 58656, 66994, 41648, 17494, 2700, 762, 0;
%e 08 : 158761, 410000, 520728, 371456, 175810, 46648, 12876, 440, 62;
%Y Row sums give A174249 or A233427(n,5).
%Y Column k=0 gives A247770.
%Y Even bisection of main diagonal gives A247076.
%Y Cf. A247739.
%K nonn,tabl
%O 0,4
%A _Alois P. Heinz_, Sep 22 2014
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