OFFSET
1,6
COMMENTS
Although each path is self-avoiding, the different paths are allowed to intersect.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..500
Ivaylo Kortezov, Sets of Paths between Vertices of a Polygon, Mathematics Competitions, Vol. 35 (2022), No. 2, ISSN:1031-7503, pp. 35-43.
FORMULA
a(n) = (n*(n-1)*(n-2)/384)*(7^(n-3) - 3*5^(n-3) + 3^(n-2) - 1).
E.g.f.: x^3*exp(x)*(exp(2*x) - 1)^3/384. - Andrew Howroyd, Mar 07 2023
EXAMPLE
PROG
(PARI) a(n) = {(n*(n-1)*(n-2)/384) * (7^(n-3) - 3*5^(n-3) + 3^(n-2) - 1)} \\ Andrew Howroyd, Mar 07 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ivaylo Kortezov, Mar 07 2023
STATUS
approved