A305324 Number of one-sided 'divisible' polyominoes of size 2^(n-1), where a 'divisible' polyomino is either a monomino (square) or a polyomino which can be separated into two identical 'divisible' polyominoes.

1, 1, 6, 90, 3356, 232283, 27964488

Offset: 1

Author

Josh Marza, May 30 2018

Keywords

• nonn
• more

Comments

a(n) is nonzero for any n >= 1. Proof is trivial by induction.

a(n) <= A000988(2^(n-1)) as any polyomino counted here is also counted in A000988.

Examples

			For n = 3 (polyominoes of size 4), the 'divisible' polyominoes are the I, O, J, L, S and Z tetrominoes. The T tetromino is not 'divisible'.
		

Crossrefs

Cf. A000988.

Extensions

Definition changed and more terms added by John Mason, Sep 20 2022