%I
%S 1,2,2,4,8,4,8,34,34,8,16,148,320,148,16,32,650,3118,3118,650,32,64,
%T 2864,30752,68480,30752,2864,64,128,12634,304618,1525558,1525558,
%U 304618,12634,128
%N Table a(m,n) read by antidiagonals, m, n >= 1, where a(m,n) is the number of divideandconquer partitions of an m X n rectangle into integer subrectangles.
%C The divideandconquer partition of an integersided rectangle is one that can be obtained by repeated bisections into adjacent integersided rectangles.
%C The table is symmetric: a(m,n) = a(n,m).
%e Table begins:
%e 1, 2, 4, 8, 16, 32, 64, ...
%e 2, 8, 34, 148, 650, 2864, 12634, ...
%e 4, 34, 320, 3118, 30752, 304618, 3022112, ...
%e 8, 148, 3118, 68480, 1525558, ...
%e 16, 650, 30752, 1525558, ...
%e 32, 2864, 304618, ...
%e 64, 12634, 3022112, ...
%e Not every partition (cf. A116694) into integer subrectangles is divideandconquer. For example, the following partition of a 3 X 3 rectangle into 5 subrectangles is not divideandconquer:
%e 112
%e 342
%e 355
%Y a(1,n) = a(n,1) = A000079(n1)
%Y a(2,n) = a(n,2) = A034999(n)
%Y Cf. A116694 (all partitions).
%K tabl,nonn,more
%O 1,2
%A _Arsenii Abdrafikov_, May 29 2013
