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A247711 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape X; triangle T(n,k), n>=0, read by rows.

%I A247711 #17 May 09 2018 10:00:13
%S A247711 1,1,5,55,1,493,8,3930,76,27207,734,9,207118,7414,157,1622723,71986,
%T A247711 2064,8,12544364,638499,22232,259,95912510,5558790,222964,3898,50,
%U A247711 732066083,47971603,2179607,49537,948,8,5616480627,410502410,20604626,564498,13889,180
%N A247711 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape X; triangle T(n,k), n>=0, read by rows.
%C A247711 Sum_{k>0} k * T(n,k) = A247744(n).
%H A247711 Alois P. Heinz, <a href="/A247711/b247711.txt">Rows n = 0..185, flattened</a>
%H A247711 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%e A247711 T(3,1) = 1:
%e A247711 ._____.
%e A247711 | ._. |
%e A247711 |_| |_|
%e A247711 |_. ._|
%e A247711 | |_| |
%e A247711 |_____|
%e A247711 .
%e A247711 Triangle T(n,k) begins:
%e A247711 00 :        1;
%e A247711 01 :        1;
%e A247711 02 :        5;
%e A247711 03 :       55,       1;
%e A247711 04 :      493,       8;
%e A247711 05 :     3930,      76;
%e A247711 06 :    27207,     734,      9;
%e A247711 07 :   207118,    7414,    157;
%e A247711 08 :  1622723,   71986,   2064,    8;
%e A247711 09 : 12544364,  638499,  22232,  259;
%e A247711 10 : 95912510, 5558790, 222964, 3898, 50;
%Y A247711 Row sums give A174249 or A233427(n,5).
%Y A247711 Columns k=0-1 give: A247775, A247828.
%Y A247711 Cf. A247744.
%K A247711 nonn,tabf
%O A247711 0,3
%A A247711 _Alois P. Heinz_, Sep 23 2014