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

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

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.

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

Crossrefs

Row sums of A126743. Cf. A000105, A125759, A125761, A125709, A125753.

Sequence in context: A334089 A326360 A123113 * A013051 A351022 A012955

Adjacent sequences: A126739 A126740 A126741 * A126743 A126744 A126745

Keyword

nonn,more

Author

David Applegate and 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