%I
%S 1,1,1,1,1,1,1,2,2,1,1,4,7,4,1,1,8,29,29,8,1,1,16,124,257,124,16,1,1,
%T 32,533,2408,2408,533,32,1,1,64,2293,22873,50128,22873,2293,64,1,1,
%U 128,9866,217969,1064576,1064576,217969,9866,128,1,1,256,42451,2078716,22734496,50796983,22734496,2078716,42451,256,1
%N Number A(n,k) of tilings of a k X n rectangle using polyominoes of shape I; square array A(n,k), n>=0, k>=0, read by antidiagonals.
%C A polyomino of shape I is a rectangle of width 1.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Polyomino">Polyomino</a>
%e Square array A(n,k) begins:
%e 1, 1, 1, 1, 1, 1, 1, ...
%e 1, 1, 2, 4, 8, 16, 32, ...
%e 1, 2, 7, 29, 124, 533, 2293, ...
%e 1, 4, 29, 257, 2408, 22873, 217969, ...
%e 1, 8, 124, 2408, 50128, 1064576, 22734496, ...
%e 1, 16, 533, 22873, 1064576, 50796983, 2441987149, ...
%e 1, 32, 2293, 217969, 22734496, 2441987149, 264719566561, ...
%Y Columns (or rows) k=07 give: A000012, A011782, A052961, A254124, A254125, A254126, A254458, A254607.
%Y Main diagonal gives: A254127.
%K nonn,tabl
%O 0,8
%A _Alois P. Heinz_, Jan 30 2015
