OFFSET
3,3
COMMENTS
Although each path is self-avoiding, the different paths are allowed to intersect.
LINKS
Ivaylo Kortezov, Sets of Non-self-intersecting Paths Connecting the Vertices of a Convex Polygon, Mathematics and Informatics, Vol. 65, No. 6, 2022.
FORMULA
a(n) = (1/3)*n*(n-1)*(n-2)*(n-3)*2^(n-15)*(4^(n-4) + 12*3^(n-4) + 54*2^(n-4) + 108) for n != 4.
EXAMPLE
a(6) = 6!/(2!2!2!2!)+6!*3/(3!3!) = 45+60 = 105; the first summand corresponds to the case of 2 two-node paths and 2 one-node paths; the second to the case of 1 three-node path and 3 one-node paths.
CROSSREFS
KEYWORD
nonn
AUTHOR
Ivaylo Kortezov, Feb 01 2023
STATUS
approved