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A247710 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape W; triangle T(n,k), n>=0, 0<=k<=max(0,floor((n-2)/2)*2) read by rows.

%I A247710 #13 Feb 06 2017 18:59:10
%S A247710 1,1,5,56,461,32,8,3558,368,80,23966,3256,696,24,8,178127,29564,6558,
%T A247710 360,80,1362597,266672,61858,4852,770,24,8,10194184,2361632,581452,
%U A247710 58732,8890,384,80,75684682,20056764,5220634,632044,97174,5968,914,24,8
%N A247710 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape W; triangle T(n,k), n>=0, 0<=k<=max(0,floor((n-2)/2)*2) read by rows.
%C A247710 Sum_{k>0} k * T(n,k) = A247743(n).
%H A247710 Alois P. Heinz, <a href="/A247710/b247710.txt">Rows n = 0..145, flattened</a>
%H A247710 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%e A247710 T(4,2) = 8:
%e A247710 ._______.        ._______.        ._______.
%e A247710 | ._____|        |_. |_. |        | ._____|
%e A247710 |_| ._| |        | |_. | |        |_| ._| |
%e A247710 | ._| ._|        | | |_| |        | ._| | |
%e A247710 |_|___| |        | |_. |_|        |_| ._| |
%e A247710 |_______| (*2)   |___|___| (*2)   |___|___| (*4)
%e A247710 Triangle T(n,k) begins:
%e A247710 00 :        1;
%e A247710 01 :        1;
%e A247710 02 :        5;
%e A247710 03 :       56;
%e A247710 04 :      461,       32,       8;
%e A247710 05 :     3558,      368,      80;
%e A247710 06 :    23966,     3256,     696,     24,     8;
%e A247710 07 :   178127,    29564,    6558,    360,    80;
%e A247710 08 :  1362597,   266672,   61858,   4852,   770,   24,   8;
%e A247710 09 : 10194184,  2361632,  581452,  58732,  8890,  384,  80;
%e A247710 10 : 75684682, 20056764, 5220634, 632044, 97174, 5968, 914, 24, 8;
%Y A247710 Row sums give A174249 or A233427(n,5).
%Y A247710 Column k=0 gives A247774.
%Y A247710 Cf. A247743.
%K A247710 nonn,tabf
%O A247710 0,3
%A A247710 _Alois P. Heinz_, Sep 23 2014