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A247706 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.

%I A247706 #18 Feb 06 2017 18:33:46
%S A247706 1,1,0,3,0,2,16,20,20,0,135,204,140,16,6,944,1432,1164,296,170,0,4814,
%T A247706 8796,8452,4068,1708,92,20,26435,58656,66994,41648,17494,2700,762,0,
%U A247706 158761,410000,520728,371456,175810,46648,12876,440,62,978044,2783560,3836254,3107308,1696312,609772,172724,18220,3160,0
%N A247706 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 A247706 Sum_{k>0} k * T(n,k) = A247739(n).
%H A247706 Alois P. Heinz, <a href="/A247706/b247706.txt">Rows n = 0..140, flattened</a>
%H A247706 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%e A247706 T(2,2) = 2:
%e A247706 .___.   .___.
%e A247706 |   |   |   |
%e A247706 | ._|   |_. |
%e A247706 |_| |   | |_|
%e A247706 |   |   |   |
%e A247706 |___|   |___| .
%e A247706 Triangle T(n,k) begins:
%e A247706 00 :      1;
%e A247706 01 :      1,      0;
%e A247706 02 :      3,      0,      2;
%e A247706 03 :     16,     20,     20,      0;
%e A247706 04 :    135,    204,    140,     16,      6;
%e A247706 05 :    944,   1432,   1164,    296,    170,     0;
%e A247706 06 :   4814,   8796,   8452,   4068,   1708,    92,    20;
%e A247706 07 :  26435,  58656,  66994,  41648,  17494,  2700,   762,   0;
%e A247706 08 : 158761, 410000, 520728, 371456, 175810, 46648, 12876, 440, 62;
%Y A247706 Row sums give A174249 or A233427(n,5).
%Y A247706 Column k=0 gives A247770.
%Y A247706 Even bisection of main diagonal gives A247076.
%Y A247706 Cf. A247739.
%K A247706 nonn,tabl
%O A247706 0,4
%A A247706 _Alois P. Heinz_, Sep 22 2014