A046091 Number of connected planar graphs with n edges.

1, 1, 1, 3, 5, 12, 30, 79, 227, 709, 2318, 8049, 29372, 112000, 444855, 1833072, 7806724, 34252145, 154342391, 712231465, 3357126655, 16119421175, 78580665333

Offset: 0

Author

Brendan McKay

Keywords

• nonn
• nice
• hard
• more

Comments

Inverse Euler transform of A343872. - Andrew Howroyd, May 05 2021

Examples

			a(3) = 3 since the three connected graphs with three edges are a path, a triangle and a "Y".
The first difference between this sequence and A002905 is for n=9 edges where we see K_{3,3}, the "utility graph".
		

Links

• B. D. McKay and A. Piperno, Practical Graph Isomorphism, II, J. Symbolic Computation, 60 (2014), pp. 94-112.
• Eric Weisstein's World of Mathematics, Planar Connected Graph.

Crossrefs

Row sums of A343873.

Column sums of A049334.

Cf. A002905, A003094, A066951, A291842, A343869, A343872.

Programs

nauty

# count graphs for the sequence by number of vertices v, sum over v afterwards
geng -c $v $n:$n | planarg -q | countg -q # Georg Grasegger, Jul 06 2023

Extensions

a(11)-a(19) from Martin Fuller using nauty by Brendan McKay, Mar 07 2015

a(20)-a(22) added by Georg Grasegger, Jul 06 2023