This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A222659 #14 May 29 2013 14:57:13 %S A222659 1,2,2,4,8,4,8,34,34,8,16,148,320,148,16,32,650,3118,3118,650,32,64, %T A222659 2864,30752,68480,30752,2864,64,128,12634,304618,1525558,1525558, %U A222659 304618,12634,128 %N A222659 Table a(m,n) read by antidiagonals, m, n >= 1, where a(m,n) is the number of divide-and-conquer partitions of an m X n rectangle into integer sub-rectangles. %C A222659 The divide-and-conquer partition of an integer-sided rectangle is one that can be obtained by repeated bisections into adjacent integer-sided rectangles. %C A222659 The table is symmetric: a(m,n) = a(n,m). %e A222659 Table begins: %e A222659 1, 2, 4, 8, 16, 32, 64, ... %e A222659 2, 8, 34, 148, 650, 2864, 12634, ... %e A222659 4, 34, 320, 3118, 30752, 304618, 3022112, ... %e A222659 8, 148, 3118, 68480, 1525558, ... %e A222659 16, 650, 30752, 1525558, ... %e A222659 32, 2864, 304618, ... %e A222659 64, 12634, 3022112, ... %e A222659 Not every partition (cf. A116694) into integer sub-rectangles is divide-and-conquer. For example, the following partition of a 3 X 3 rectangle into 5 sub-rectangles is not divide-and-conquer: %e A222659 112 %e A222659 342 %e A222659 355 %Y A222659 a(1,n) = a(n,1) = A000079(n-1) %Y A222659 a(2,n) = a(n,2) = A034999(n) %Y A222659 Cf. A116694 (all partitions). %K A222659 tabl,nonn,more %O A222659 1,2 %A A222659 _Arsenii Abdrafikov_, May 29 2013