A371536 a(n) is the number of unobscured pentagons remaining after completing step n.

1, 1, 6, 41, 186

Offset: 1

Author

Gavin Lupo, Mar 26 2024

Keywords

• nonn
• more

Comments

Start with a single regular pentagon. The pentagon fractal is constructed by taking with the previous completed step, and overlapping it in its entirety to each vertex (excluding the top vertex as they overlap completely). Once constructed, any unobscured pentagons within are counted. "Unobscured" means no lines cross through it, and its shape is regular. See links for images.

Examples

			Start with a(1) = 1 unobscured pentagon. For the next step, take step 1's entire shape and place it at each vertex. Although the total number of pentagons is 5, only 1 unobscured pentagon remains, so a(2) = 1.
		

Links

• Gavin Lupo, Pentagon Construction, the initial steps
• Gavin Lupo, Step 5