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

1,3

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).

Links

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

Example

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

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).

Sequence in context: A207620 A354766 A207622 * A073017 A296092 A259111

Adjacent sequences: A335570 A335571 A335572 * A335574 A335575 A335576

Keyword

nonn

Author

John Mason, Jan 26 2021

Status

approved