A379626 Sum of the widths of the free polyominoes with n cells.

1, 1, 3, 9, 29, 91, 322, 1206, 4600, 17931, 70577, 279652, 1110758, 4424120, 17647314, 70484576

Offset

1,3

Comments

The width here is the shorter of the two dimensions.

Links

Table of n, a(n) for n=1..16.

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 is only one free tetromino of width 1 and there are four free tetrominoes of width 2, hence the sum of the widths is 1 + 2 + 2 + 2 + 2 = 9, so a(4) = 9.

Crossrefs

Row sums of A379637.

Cf. A000105, A379623, A379625, A379627, A379629.

Sequence in context: A262253 A303546 A135142 * A195624 A098589 A024744

Adjacent sequences: A379623 A379624 A379625 * A379627 A379628 A379629

Keyword

nonn,more,new

Author

Omar E. Pol, Jan 16 2025

Extensions

a(15)-a(16) from Pontus von Brömssen, Jan 17 2025

Status

approved