1,2

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.

MacKinnon incorrectly implies that the sequence is 1,6,44.

MacKinnon only allows polyominoes with >= n cells, leading to A125709 and A125753.

The polyominoes with < 2n cells are uninteresting, leading to A126742 and A126743.

Comment from Peter Pleasants, Feb 18 2007: 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.

N. MacKinnon, Some thoughts on polyomino tilings, Math. Gaz., 74 (1990), 31-33.

S. Rinaldi and D. G. Rogers, Indecomposability: polyominoes and polyomino tilings, Math. Gaz., to appear, 2008.

David Applegate, Pictures of all 2-indecomposable polyominoes

David Applegate, Pictures of all 3-indecomposable polyominoes

David Applegate, Pictures of all 4-indecomposable polyominoes

David Applegate, Pictures of all 5-indecomposable polyominoes

David Applegate, Pictures of all 6-indecomposable polyominoes (gzipped)

a(n) = A125709(n) + Sum_{i=1..n-1} A000105(i).

The six 2-indecomposable polyominoes:

......................X.

X..XX..XXX..XX..XXX..XXX

.............X...X....X.

Row sums of A125761. Cf. A125709, A125753, A126742, A126743, A000105.

Adjacent sequences: A125756 A125757 A125758 this_sequence A125760 A125761 A125762

Sequence in context: A079568 A063090 A108432 this_sequence A062819 A092336 A003423

nonn,more

David Applegate (david(AT)research.att.com) and njas, Feb 05 2007

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

a(6) and a(7) from David Applegate (david(AT)research.att.com), Feb 16 2007