A379629 Sum of the lengths of the free polyominoes with n cells.

1, 2, 5, 15, 41, 139, 474, 1773, 6686, 26043, 101814, 402297, 1593124, 6332329, 25200575, 100462874, 400908688, 1601541747

Offset

1,2

Comments

The length here is the longer of the two dimensions.

Links

Table of n, a(n) for n=1..18.

Index entries for sequences related to polyominoes.

Example

For n = 4 the free polyominoes with four cells are also called free tetrominoes.
The five free tetrominoes are as shown below:
                                     _
             _       _       _      |_|
    _ _     |_|     |_|_    |_|_    |_|
   |_|_|    |_|_    |_|_|   |_|_|   |_|
   |_|_|    |_|_|     |_|   |_|     |_|
.
There are no free tetrominoes of length 1, there is only one free tetromino of length 2, there are three free tetrominoes of length 3 and there is only one free tetromino of length 4, hence the sum of the lengths is 0 + 2 + 3 + 3 + 3 + 4 = 15, so a(4) = 15.

Crossrefs

Row sums of A379638.

Cf. A000105, A379624, A379625, A379626, A379627.

Sequence in context: A076865 A190140 A006649 * A392425 A392442 A303980

Adjacent sequences: A379626 A379627 A379628 * A379630 A379631 A379632

Keyword

nonn,more

Author

Omar E. Pol, Jan 16 2025

Extensions

a(13)-a(16) from Pontus von Brömssen, Jan 17 2025

a(17)-a(18) (based on A379624 b-file) from Pontus von Brömssen, Feb 21 2025

Status

approved