Number of connected unlabeled graphs with n edges

unlabeled_connected_balanced.jl

using Graphs, Combinatorics
#   [861a8166] Combinatorics v1.0.2
#   [86223c79] Graphs v1.7.0

function all_balanced_graphs(n)
    S = Set{SimpleGraph}()
    all_balanced_graphs!(S, n)
end

function all_balanced_graphs!(S, n)
    possible_gs = combinations(1:binomial(n, 2), n)
    e_labels = collect(combinations(1:n, 2))
    for p in possible_gs
        g = SimpleGraph(n)
        for ev in e_labels[p]
            add_edge!(g, ev...)
        end
        push_graph!(S, g)
    end
    S
end

function push_graph!(set::AbstractSet, g::AbstractGraph)
    for e in set
        if Graphs.Experimental.has_isomorph(g, e)
            return set
        end
    end
    push!(set, g)
end

# https://oeis.org/A116508
gl = all_balanced_graphs.(1:7)

# https://oeis.org/A057500
gc = map(g -> filter(is_connected, g), gl)

# this sequence
length.(gc)