A342269 Take a regular (2*n+1)-gon with all diagonals drawn; a(n) = number of edges in next-to-largest cell.

3, 5, 6, 6, 8, 7, 8, 8, 7, 8, 8, 8, 11, 10, 8, 9, 10, 8, 10, 14, 9, 10, 10, 12, 12, 10, 10, 12, 12, 12, 12, 10, 10, 11, 12, 12, 10, 10, 10, 10, 12, 10, 10, 12, 13, 12, 12, 11, 12, 12, 12, 12, 12, 10, 10, 12, 14, 14, 12, 12, 12, 10, 12, 12, 14, 12, 10, 12, 12

Offset: 2

Author

Scott R. Shannon and N. J. A. Sloane, Mar 07 2021

Keywords

• nonn
• more

Comments

The largest cell has 2*n+1 sides, this is the runner-up.

It can be read off the rows of A331450.

It would be nice to know how fast this sequence grows. Is it unbounded?

Links

• Scott R. Shannon, Image for a(2) = 3. The 5-gon has a next-to-largest cell with 3 edges.
• Scott R. Shannon, Image for a(3) = 5. The 7-gon has a next-to-largest cell with 5 edges.
• Scott R. Shannon, Image for a(4) = 6. The 9-gon has a next-to-largest cell with 6 edges.
• Scott R. Shannon, Image for a(7) = 7. The 15-gon has a next-to-largest cell with 7 edges.
• Scott R. Shannon, Image for a(6) = 8. The 13-gon has a next-to-largest cell with 8 edges.
• Scott R. Shannon, Image for a(17) = 9. The 35-gon has a next-to-largest cell with 9 edges.
• Scott R. Shannon, Image for a(15) = 10. The 31-gon has a next-to-largest cell with 10 edges.
• Scott R. Shannon, Image for a(14) = 11. The 29-gon has a next-to-largest cell with 11 edges.
• Scott R. Shannon, Image for a(25) = 12. The 51-gon has a next-to-largest cell with 12 edges.

Crossrefs

Cf. A331450, A342236, A341735, A341729, A342222.