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%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
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