%I #10 Jun 11 2022 13:48:37
%S 0,1,2,5,15,47,156,527,1826,6407,22762,81587,294711,1070973,3912808,
%T 14358493,52893647,195498831,724704974,2693397035,10033263089,
%U 37452388361,140063288728
%N Number of subgraphs of the directed square lattice with n vertices and all vertices reachable from the origin.
%C Similar to A344571 but here n is the number of vertices.
%F a(n) >= 2*a(n-1) for n > 0.
%e In the following examples, the origin is in the bottom left corner and graph edges are directed upwards and to the right.
%e The a(1) = 1 graph is:
%e .
%e The a(2) = 2 graphs are:
%e | __
%e .
%e The a(3) = 5 graphs are:
%e | __
%e | | __.__ __| |__
%e .
%e The a(4) = 15 graphs are:
%e | __
%e | | |__ __| __.__ | __
%e | | | | | |__ |__
%e .
%e __ | __
%e __.__.__ __.__| __|__ __| __| |__.__ |__| |__|
%e .
%e Other examples with 5, 6, and 7 vertices respectively include:
%e | __.__ __|__|
%e |__| |__.__| |__|
%Y Cf. A344571.
%K nonn,more
%O 0,3
%A _Roman Hros_, Apr 18 2022