OFFSET
1,5
COMMENTS
This sequence is log-superadditive, i.e., a(m+n) >= a(m)*a(n). By Fekete's subadditive lemma, it follows that the limit of a(n)^(1/n) exists and equals the supremum of a(n)^(1/n). - Pontus von Brömssen, Mar 03 2022
a(11) >= 381, because the complete 5-partite graph K_{1,1,3,3,3} has 381 maximal planar subgraphs.
FORMULA
a(m+n) >= a(m)*a(n).
Lim_{n->oo} a(n)^(1/n) >= 381^(1/11) = 1.71644... .
EXAMPLE
For 4 <= n <= 9, a(n) = binomial(n,4) = A000332(n) and the complete graph is optimal, but a(10) = 211 > 210 = binomial(10,4) with the optimal graph being the complete 6-partite graph K_{1,1,1,1,3,3}. The optimal graph is unique when 5 <= n <= 10.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Pontus von Brömssen, Mar 05 2021
STATUS
approved