A125759 Number of n-indecomposable polyominoes.

1, 6, 34, 448, 13384, 684236, 52267569

Offset

1,2

Comments

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.

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

Links

Table of n, a(n) for n=1..7.

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)

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

Simone Rinaldi and D. G. Rogers, Indecomposability: polyominoes and polyomino tilings, The Mathematical Gazette 92.524 (2008): 193-204.

Formula

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

Example

The six 2-indecomposable polyominoes:
......................X.
X..XX..XXX..XX..XXX..XXX
.............X...X....X.

Crossrefs

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

Sequence in context: A245466 A362627 A284330 * A062819 A230246 A092336

Adjacent sequences: A125756 A125757 A125758 * A125760 A125761 A125762

Keyword

nonn,more

Author

David Applegate and N. J. A. Sloane, Feb 05 2007

Extensions

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

a(6) and a(7) from David Applegate, Feb 16 2007

Status

approved