A335573 a(n) is the number of fixed polyominoes corresponding to the free polyomino represented by A246521(n).

1, 1, 2, 4, 2, 8, 1, 4, 4, 2, 8, 4, 4, 8, 8, 8, 4, 4, 8, 4, 1, 2, 4, 8, 8, 8, 2, 8, 8, 8, 8, 8, 4, 8, 4, 8, 8, 8, 8, 4, 4, 8, 4, 8, 8, 8, 4, 4, 4, 4, 8, 8, 4, 8, 4, 4, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 4, 8, 2, 8, 8, 8, 8, 8, 4, 4, 8, 4, 8, 8, 8, 8, 8, 8, 8

Offset: 1

Author

John Mason, Jan 26 2021

Keywords

• nonn

Comments

Each free polyomino represented by a number in A246521 may correspond to 1, 2, 4 or 8 different fixed polyominoes, generated by rotation or reflection.

In the sequence A246521, the size n polyominoes start at position j = 1 + Sum_{i=0..n-1} A000105(i) and end at position k = Sum_{i=0..n} A000105(i). Therefore, the number of fixed polyominoes, A001168(n), is equal to Sum_{i=j..k} a(i).

Examples

			The size 4 L-shaped polyomino represented by A246521(6) will generate 8 fixed polyominoes.
		

Links

• Pontus von Brömssen, Table of n, a(n) for n = 1..6474 (polyominoes with up to 10 cells).

Crossrefs

Cf. A000105 (number of free polyominoes of size n).

Cf. A001168 (number of fixed polyominoes of size n).

Cf. A246521 (list of free polyominoes in binary coding).