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A247705 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape N; triangle T(n,k), n>=0, read by rows.

%I A247705 #15 Feb 07 2017 10:15:32
%S A247705 1,1,5,48,8,423,68,10,3082,832,84,8,18998,7624,1230,88,10,133083,
%T A247705 65360,14390,1732,116,8,965175,555236,150876,23184,2196,108,6,6907447,
%U A247705 4531744,1454292,275320,33807,2616,124,4,48357538,36466396,13354738,3012116,457360,46872,3086,104,2
%N A247705 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape N; triangle T(n,k), n>=0, read by rows.
%C A247705 Sum_{k>0} k * T(n,k) = A247738(n).
%H A247705 Alois P. Heinz, <a href="/A247705/b247705.txt">Rows n = 0..160, flattened</a>
%H A247705 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%e A247705 T(3,1) = 8:
%e A247705 ._____.        .___._.
%e A247705 | ._. |        | ._| |
%e A247705 |_| |_|        | | ._|
%e A247705 | ._| |        | | | |
%e A247705 | |   |        |_|_| |
%e A247705 |_|___| (*4)   |_____| (*4)  .
%e A247705 Triangle T(n,k) begins:
%e A247705 00 :      1;
%e A247705 01 :      1;
%e A247705 02 :      5;
%e A247705 03 :     48,      8;
%e A247705 04 :    423,     68,     10;
%e A247705 05 :   3082,    832,     84,     8;
%e A247705 06 :  18998,   7624,   1230,    88,   10;
%e A247705 07 : 133083,  65360,  14390,  1732,  116,   8;
%e A247705 08 : 965175, 555236, 150876, 23184, 2196, 108,  6;
%Y A247705 Row sums give A174249 or A233427(n,5).
%Y A247705 Column k=0 gives A247769.
%Y A247705 Cf. A247738.
%K A247705 nonn,tabf
%O A247705 0,3
%A A247705 _Alois P. Heinz_, Sep 22 2014