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A247702 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape F; triangle T(n,k), n>=0, 0<=k<=max(delta_{3,n},floor((n-2)/2)*2), read by rows.

%I A247702 #25 Feb 06 2017 18:40:36
%S A247702 1,1,5,52,4,437,60,4,3342,584,80,21734,5372,818,24,2,155685,49540,
%T A247702 8800,620,44,1153475,439780,92500,10140,856,28,2,8422634,3726836,
%U A247702 914142,127596,13338,760,48,60853524,30683256,8544440,1425320,176156,14404,1078,32,2
%N A247702 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape F; triangle T(n,k), n>=0, 0<=k<=max(delta_{3,n},floor((n-2)/2)*2), read by rows.
%C A247702 Sum_{k>0} k * T(n,k) = A247735(n).
%H A247702 Alois P. Heinz, <a href="/A247702/b247702.txt">Rows n = 0..150, flattened</a>
%H A247702 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%e A247702 T(3,1) = 4:
%e A247702 ._____.  ._____.  ._____.  ._____.
%e A247702 |_.   |  |   ._|  | ._. |  | ._. |
%e A247702 | |___|  |___| |  |_| |_|  |_| |_|
%e A247702 |_. ._|  |_. ._|  | .___|  |___. |
%e A247702 | |_| |  | |_| |  |_|   |  |   |_|
%e A247702 |_____|  |_____|  |_____|  |_____| .
%e A247702 Triangle T(n,k) begins:
%e A247702 00 :        1;
%e A247702 01 :        1;
%e A247702 02 :        5;
%e A247702 03 :       52,        4;
%e A247702 04 :      437,       60,       4;
%e A247702 05 :     3342,      584,      80;
%e A247702 06 :    21734,     5372,     818,      24,      2;
%e A247702 07 :   155685,    49540,    8800,     620,     44;
%e A247702 08 :  1153475,   439780,   92500,   10140,    856,    28,    2;
%e A247702 09 :  8422634,  3726836,  914142,  127596,  13338,   760,   48;
%e A247702 10 : 60853524, 30683256, 8544440, 1425320, 176156, 14404, 1078, 32, 2;
%Y A247702 Row sums give A174249 or A233427(n,5).
%Y A247702 Column k=0 gives A247766.
%Y A247702 Cf. A247735.
%K A247702 nonn,tabf
%O A247702 0,3
%A A247702 _Alois P. Heinz_, Sep 22 2014