A126742 Number of n-indecomposable polyominoes with at least 2n cells.

0, 2, 13, 284, 13375, 660690, 51941832

Offset: 1

Author

David Applegate and 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.

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.
Only the last two have >= 4 cells, so a(2) = 2.
		

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 A126743. Cf. A000105, A125759, A125761, A125709, A125753.

Extensions

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

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