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A125759 Number of n-indecomposable polyominoes.

%I A125759 #13 Jan 23 2019 20:01:00
%S A125759 1,6,34,448,13384,684236,52267569
%N A125759 Number of n-indecomposable polyominoes.
%C A125759 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 A125759 MacKinnon incorrectly implies that the sequence is 1,6,44.
%C A125759 MacKinnon only allows polyominoes with >= n cells, leading to A125709 and A125753.
%C A125759 The polyominoes with < 2n cells are uninteresting, leading to A126742 and A126743.
%C A125759 There is a sense in which n-decomposable polyominoes with >3n-2 cells are also uninteresting: they are precisely the "n-spiders", where an n-spider is a polyomino with a cell whose removal splits it into 4 components each with <n cells. - Peter Pleasants, Feb 18 2007
%H A125759 David Applegate, <a href="/A125759/a125759_2.txt">Pictures of all 2-indecomposable polyominoes</a>
%H A125759 David Applegate, <a href="/A125759/a125759_3.txt">Pictures of all 3-indecomposable polyominoes</a>
%H A125759 David Applegate, <a href="/A125759/a125759_4.txt">Pictures of all 4-indecomposable polyominoes</a>
%H A125759 David Applegate, <a href="/A125759/a125759_5.txt">Pictures of all 5-indecomposable polyominoes</a>
%H A125759 David Applegate, <a href="/A125759/a125759_6.txt.gz">Pictures of all 6-indecomposable polyominoes (gzipped)</a>
%H A125759 N. MacKinnon, <a href="http://www.jstor.org/stable/3618845">Some thoughts on polyomino tilings</a>, Math. Gaz., 74 (1990), 31-33.
%H A125759 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.
%F A125759 a(n) = A125709(n) + Sum_{i=1..n-1} A000105(i).
%e A125759 The six 2-indecomposable polyominoes:
%e A125759 ......................X.
%e A125759 X..XX..XXX..XX..XXX..XXX
%e A125759 .............X...X....X.
%Y A125759 Row sums of A125761. Cf. A125709, A125753, A126742, A126743, A000105.
%K A125759 nonn,more
%O A125759 1,2
%A A125759 _David Applegate_ and _N. J. A. Sloane_, Feb 05 2007
%E A125759 a(4) and a(5) from Peter Pleasants, Feb 13 2007
%E A125759 a(6) and a(7) from _David Applegate_, Feb 16 2007