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A247704 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.

%I A247704 #14 Feb 07 2017 10:14:07
%S A247704 1,1,0,3,0,2,36,16,4,0,177,220,100,0,4,1300,1720,816,144,26,0,8866,
%T A247704 11152,5616,1784,524,0,8,54849,85016,51116,18380,4656,584,88,0,372943,
%U A247704 622732,448744,189360,52130,8948,1908,0,16,2466986,4528336,3670116,1806160,582250,127140,22206,1912,248,0
%N A247704 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 A247704 Sum_{k>0} k * T(n,k) = A247737(n).
%H A247704 Alois P. Heinz, <a href="/A247704/b247704.txt">Rows n = 0..140, flattened</a>
%H A247704 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%e A247704 T(2,2) = 2:
%e A247704 .___.   .___.
%e A247704 | ._|   |_. |
%e A247704 | | |   | | |
%e A247704 | | |   | | |
%e A247704 |_| |   | |_|
%e A247704 |___|   |___| .
%e A247704 Triangle T(n,k) begins:
%e A247704 00 :      1;
%e A247704 01 :      1,      0;
%e A247704 02 :      3,      0,      2;
%e A247704 03 :     36,     16,      4,      0;
%e A247704 04 :    177,    220,    100,      0,     4;
%e A247704 05 :   1300,   1720,    816,    144,    26,    0;
%e A247704 06 :   8866,  11152,   5616,   1784,   524,    0,    8;
%e A247704 07 :  54849,  85016,  51116,  18380,  4656,  584,   88,  0;
%e A247704 08 : 372943, 622732, 448744, 189360, 52130, 8948, 1908,  0, 16;
%Y A247704 Row sums give A174249 or A233427(n,5).
%Y A247704 Column k=0 gives A247768.
%Y A247704 Cf. A247737.
%K A247704 nonn,tabl
%O A247704 0,4
%A A247704 _Alois P. Heinz_, Sep 22 2014