A156228 Number of lakes in Conway's Game of Life with 8*n cells.

1, 0, 1, 1, 4, 7, 31, 98, 446, 1894, 9049, 43151

Offset: 1

Author

Nathaniel Johnston, Feb 06 2009

Keywords

• nonn
• hard
• more

Comments

a(n) is also the number of walks of length 4*n on a 2D lattice with the properties that: it turns 90 degrees after every step of length 1, it is a closed loop (i.e., it ends where it started) and it never crosses itself.

In A266549, the walks are allowed to continue straight ahead. - Pontus von Brömssen, May 06 2025

Examples

			a(2) = 0 because there are no lakes with 16 cells.
		

Links

• Nathaniel Johnston, Counting Lakes
• LifeWiki, Lakes

Crossrefs

Cf. A019473, A266549, A337550.

Extensions

a(11) and a(12) added by Nathaniel Johnston, Mar 09 2009