%I #11 Aug 27 2022 03:11:41
%S 1,0,1,1,4,7,31,98,446,1894,9049,43151
%N Number of lakes in Conway's Game of Life with 8*n cells.
%C 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.
%H Nathaniel Johnston, <a href="http://www.nathanieljohnston.com/2009/02/counting-lakes/">Counting Lakes</a>
%H LifeWiki, <a href="http://www.conwaylife.com/wiki/Lake">Lakes</a>
%e a(2) = 0 because there are no lakes with 16 cells.
%Y Cf. A019473
%K hard,more,nonn
%O 1,5
%A _Nathaniel Johnston_, Feb 06 2009
%E a(11) and a(12) added by _Nathaniel Johnston_, Mar 09 2009