A125709 - OEIS

%I #9 Jul 19 2020 04:05:54

%S 1,5,32,444,13375,684215,52267513

%N Number of n-indecomposable polyominoes with at least n cells.

%C A polyomino is called n-indecomposable if it cannot be partitioned (along cell boundaries) into two or more polyominoes each with at least n cells.

%C MacKinnon incorrectly gives a(3) = 42.

%C For full lists of drawings of these polyominoes for n <= 6, see the links in A125759.

%H N. MacKinnon, <a href="http://www.jstor.org/stable/3618845">Some thoughts on polyomino tilings</a>, Math. Gaz., 74 (1990), 31-33.

%H Simone Rinaldi and D. G. Rogers, <a href="http://www.jstor.org/stable/27821767">Indecomposability: polyominoes and polyomino tilings</a>, The Mathematical Gazette 92.524 (2008): 193-204.

%e The five 2-indecomposable polyominoes:

%e ...................X.

%e XX..XXX..XX..XXX..XXX

%e ..........X...X....X.

%Y Row sums of A125753. Cf. A125759, A125761, A126742, A126743.

%K nonn,more

%O 1,2

%A _N. J. A. Sloane_, Feb 01 2007

%E a(4) and a(5) from Peter Pleasants, Feb 13 2007

%E a(6) and a(7) from _David Applegate_, Feb 16 2007