%I #14 Feb 26 2023 20:10:55
%S 1,4,21,192,2035,27407
%N Number of sets of integer-sided rectangular pieces that can tile an n X n square.
%e The a(3) = 21 possible sets of pieces that can tile a 3 X 3 square are given in the table below. (Each column on the right gives a set of pieces.)
%e .
%e length X width | number of pieces
%e ---------------+------------------------------------------
%e 3 X 3 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e 2 X 3 | 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e 2 X 2 | 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0
%e 1 X 3 | 0 1 0 0 1 1 0 0 0 3 2 2 1 1 1 1 0 0 0 0 0
%e 1 X 2 | 0 0 1 0 1 0 2 1 0 0 1 0 3 2 1 0 4 3 2 1 0
%e 1 X 1 | 0 0 1 3 0 2 1 3 5 0 1 3 0 2 4 6 1 3 5 7 9
%Y Main diagonal of A360629.
%Y Cf. A034295 (square pieces).
%K nonn,more
%O 1,2
%A _Pontus von Brömssen_, Feb 14 2023