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%I #40 Mar 16 2023 13:42:20
%S 1,1,8,322,70878,84231996,535236230270,18100579400986674,
%T 3250879178100782348462,3097923464622249063718465240,
%U 15657867573050419014814618149422562,419678195343896524683571751908598967042082,59647666241586874002530830848160043213559146735474
%N Number of ways of dividing an n X n square into rectangles of integer side lengths.
%H David A. Klarner and Spyros S. Magliveras, <a href="https://doi.org/10.1016/S0195-6698(88)80062-3">The number of tilings of a block with blocks</a>, European Journal of Combinatorics 9 (1988), 317-330.
%H Joshua Smith and Helena Verrill, <a href="/A116694/a116694.pdf">On dividing rectangles into rectangles</a>
%F a(n) = A116694(n,n) for n > 0.
%e For n=2 the a(2) = 8 ways to divide are:
%e ._ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
%e | | | | | |_ _| | |_| |_| | |_ _| |_|_| |_|_|
%e |_ _| |_|_| |_ _| |_|_| |_|_| |_|_| |_ _| |_|_|
%Y Main diagonal of A116694 and of A333476.
%Y Cf. A034999.
%K nonn
%O 0,3
%A _Matthew C. Russell_, Apr 23 2012
%E a(11)-a(12) from _Steve Butler_, Mar 14 2014