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

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

Offset: 1

Author

N. J. A. Sloane, Feb 01 2007

Keywords

• nonn
• more

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.

Examples

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

Links

• 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.

Crossrefs

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

Extensions

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

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