

A125759


Number of nindecomposable polyominoes.


7




OFFSET

1,2


COMMENTS

A polyomino is called nindecomposable 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 ndecomposable polyominoes with >3n2 cells are also uninteresting: they are precisely the "nspiders", where an nspider 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 2indecomposable polyominoes
David Applegate, Pictures of all 3indecomposable polyominoes
David Applegate, Pictures of all 4indecomposable polyominoes
David Applegate, Pictures of all 5indecomposable polyominoes
David Applegate, Pictures of all 6indecomposable polyominoes (gzipped)
N. MacKinnon, Some thoughts on polyomino tilings, Math. Gaz., 74 (1990), 3133.
Simone Rinaldi and D. G. Rogers, Indecomposability: polyominoes and polyomino tilings, The Mathematical Gazette 92.524 (2008): 193204.


FORMULA

a(n) = A125709(n) + Sum_{i=1..n1} A000105(i).


EXAMPLE

The six 2indecomposable 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: A337350 A245466 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



