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A247709 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape V; triangle T(n,k), n>=0, 0<=k<=max(0,n-2+delta_{n,3}), read by rows.

%I A247709 #14 Feb 06 2017 19:00:49
%S A247709 1,1,5,38,16,2,329,152,20,2614,1224,160,8,17400,8656,1714,168,12,
%T A247709 122843,72104,17280,2300,158,4,901647,598444,168422,25872,2284,108,4,
%U A247709 6662758,4770520,1479850,260672,29166,2256,124,8,48492622,37416964,12800398,2601524,351578,32840,2182,100,4
%N A247709 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape V; triangle T(n,k), n>=0, 0<=k<=max(0,n-2+delta_{n,3}), read by rows.
%C A247709 Sum_{k>0} k * T(n,k) = A247742(n).
%H A247709 Alois P. Heinz, <a href="/A247709/b247709.txt">Rows n = 0..145, flattened</a>
%H A247709 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%e A247709 T(3,2) = 2:
%e A247709 ._____.    ._____.
%e A247709 | .___|    |___. |
%e A247709 | | ._|    |_. | |
%e A247709 |_| | |    | | |_|
%e A247709 |___| |    | |___|
%e A247709 |_____|    |_____| .
%e A247709 Triangle T(n,k) begins:
%e A247709 00 :        1;
%e A247709 01 :        1;
%e A247709 02 :        5;
%e A247709 03 :       38,       16,        2;
%e A247709 04 :      329,      152,       20;
%e A247709 05 :     2614,     1224,      160,       8;
%e A247709 06 :    17400,     8656,     1714,     168,     12;
%e A247709 07 :   122843,    72104,    17280,    2300,    158,     4;
%e A247709 08 :   901647,   598444,   168422,   25872,   2284,   108,    4;
%e A247709 09 :  6662758,  4770520,  1479850,  260672,  29166,  2256,  124,   8;
%e A247709 10 : 48492622, 37416964, 12800398, 2601524, 351578, 32840, 2182, 100, 4;
%Y A247709 Row sums give A174249 or A233427(n,5).
%Y A247709 Column k=0 gives A247773.
%Y A247709 Cf. A247742.
%K A247709 nonn,tabf
%O A247709 0,3
%A A247709 _Alois P. Heinz_, Sep 22 2014