OFFSET

1,2

COMMENTS

Here G_n = {V_n, E_n}, V_n = {v_1, v_2, ..., v_n}, E_n = {e_1, e_2, ..., e_{n-1}, f_1, f_2, ..., f_{n-1}}. For all i, e_i = f_i = v_iv_{i+1} although e_i and f_i are considered distinct.

Given an undirected multigraph G = (V,E) with labeled edges, its partition into strokes is a collection of directed edge-disjoint paths (viewed as sets of directed edges) on V such that (i) union of any two paths is not a path; (ii) union of corresponding undirected paths is E.

FORMULA

For n >= 6, a(n) = 13*a(n-1) - 22*a(n-2) - 88*a(n-3) + 112*a(n-4).

O.g.f.: x * (1-2*x)^2 * (1 - 3*x - 14*x^2) / (1 - 13*x + 22*x^2 + 88*x^3 - 112*x^4).

CROSSREFS

KEYWORD

nonn

AUTHOR

Yasutoshi Kohmoto and Max Alekseyev, Jul 18 2022

STATUS

approved