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

3,2

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.

Links

John Mason, Table of n, a(n) for n = 3..400

John Mason, Java program containing formulas

Example

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

Crossrefs

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

Sequence in context: A000782 A148775 A148776 * A127385 A152880 A259441

Adjacent sequences: A353064 A353065 A353066 * A353068 A353069 A353070

Keyword

nonn

Author

John Mason, Apr 21 2022

Status

approved