A353028 Number of subgraphs of the directed square lattice with n vertices and all vertices reachable from the origin.
0, 1, 2, 5, 15, 47, 156, 527, 1826, 6407, 22762, 81587, 294711, 1070973, 3912808, 14358493, 52893647, 195498831, 724704974, 2693397035, 10033263089, 37452388361, 140063288728
Offset: 0
Examples
In the following examples, the origin is in the bottom left corner and graph edges are directed upwards and to the right.
The a(1) = 1 graph is:
.
The a(2) = 2 graphs are:
| __
.
The a(3) = 5 graphs are:
| __
| | __.__ __| |__
.
The a(4) = 15 graphs are:
| __
| | |__ __| __.__ | __
| | | | | |__ |__
.
__ | __
__.__.__ __.__| __|__ __| __| |__.__ |__| |__|
.
Other examples with 5, 6, and 7 vertices respectively include:
| __.__ __|__|
|__| |__.__| |__|
Crossrefs
Cf. A344571.
Formula
a(n) >= 2*a(n-1) for n > 0.
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