login
Number of sets of integer-sided rectangular pieces that can tile an n X n square.
7

%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