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

1, 1, 6, 41, 186

Offset

1,3

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.

Links

Table of n, a(n) for n=1..5.

Gavin Lupo, Pentagon Construction, the initial steps

Gavin Lupo, Step 5

Example

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.

Crossrefs

Sequence in context: A043069 A257602 A135232 * A291890 A217326 A196433

Adjacent sequences: A371533 A371534 A371535 * A371537 A371538 A371539

Keyword

nonn,more

Author

Gavin Lupo, Mar 26 2024

Status

approved