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

0,3

Comments

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

Links

Table of n, a(n) for n=0..22.

Formula

a(n) >= 2*a(n-1) for n > 0.

Example

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.

Sequence in context: A149916 A149917 A149918 * A149919 A149920 A149921

Adjacent sequences: A353025 A353026 A353027 * A353029 A353030 A353031

Keyword

nonn,more

Author

Roman Hros, Apr 18 2022

Status

approved