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, 281750598, 1127181327

Offset: 1

Author

Omar E. Pol, Jan 16 2025

Keywords

• nonn
• more

Comments

The width here is the shorter of the two dimensions.

Examples

			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.
		

Links

• Index entries for sequences related to polyominoes.

Crossrefs

Row sums of A379637.

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

Extensions

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

a(17)-a(18) from John Mason, Feb 16 2025