A379627 Total area of the bounding boxes of the free polyominoes with n cells.

1, 2, 7, 26, 95, 353, 1387, 5699, 23592, 99020, 415796, 1748722, 7336978, 30741661, 128510698, 536268877, 2233642396, 9288889882

Offset: 1

Author

Omar E. Pol, Jan 07 2025

Keywords

• nonn
• more

Comments

a(n) is also the total sum of all products of length and width of the free polyominoes with n cells.

Examples

			Illustration for n = 4:
The free polyominoes with four cells are also called free tetrominoes.
The five free tetrominoes are as shown below:
    _
   |_|     _       _       _
   |_|    |_|     |_|_    |_|_     _ _
   |_|    |_|_    |_|_|   |_|_|   |_|_|
   |_|    |_|_|     |_|   |_|     |_|_|
.
The bounding boxes are respectively as shown below:
    _
   | |     _ _     _ _     _ _
   | |    |   |   |   |   |   |    _ _
   | |    |   |   |   |   |   |   |   |
   |_|    |_ _|   |_ _|   |_ _|   |_ _|
.
  4 X 1   3 X 2   3 X 2   3 X 2   2 X 2
.
The total area of the bounding boxes is 4 + 6 + 6 + 6 + 4 = 26, so a(4) = 26.
.
		

Links

• Index entries for sequences related to polyominoes.

Crossrefs

Cf. A000105, A057766, A379623, A379624, A379628.

Formula

a(n) = A057766(n) + A379628(n).

Extensions

a(7)-a(16) from Pontus von Brömssen, Jan 11 2025

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