A125709 Number of n-indecomposable polyominoes with at least n cells.

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

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 gives a(3) = 42.

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

Links

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

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.

Example

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

Crossrefs

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

Sequence in context: A185136 A014374 A185336 * A363314 A203112 A349099

Adjacent sequences: A125706 A125707 A125708 * A125710 A125711 A125712

Keyword

nonn,more

Author

N. J. A. Sloane, Feb 01 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