A125759 Number of n-indecomposable polyominoes.

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

Offset: 1

Author

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

Examples

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

Links

• 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.

Crossrefs

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

Formula

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

Extensions

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

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

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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