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

Author

Roman Hros, Apr 18 2022

Keywords

• nonn
• more

Comments

Similar to A344571 but here n is the number of vertices.

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.