A353067 a(n) is the number of free polyominoes of width 3 and size n.

1, 3, 8, 23, 71, 193, 490, 1221, 3011, 7393, 18025, 43847, 106206, 256851, 619642, 1493272, 3593527, 8641624, 20764212, 49869733, 119716469, 287306693, 689316717, 1653539600, 3965895220, 9510880953, 22806565004, 54685294862, 131116579494, 314360235644

Offset: 3

Author

John Mason, Apr 21 2022

Keywords

• nonn

Comments

The sequence can be generated using a series of recursive formulas in a fashion similar to A352720. This latter requires around 500 formula lines, whereas a(n) requires about 62000 lines.

Examples

			a(3) = 1 because of the straight tromino.
a(4) = 3 because of the following tetrominoes:
  O     O    OO
  OOO  OOO  OO
		

Links

• John Mason, Table of n, a(n) for n = 3..400
• John Mason, Java program containing formulas

Crossrefs

Cf. A000105, A352720 (width 2 and size n), A354850 (width 4 and size n).