OFFSET
0,5
COMMENTS
In a convex n-gon, the number of paths using k non-repeated vertices and fewer than 3 vertices (2 sides) in a row.
FORMULA
T(n,k) = n*(A340106(n-1,k-1) - S(n-2,k-2)) except for T(n,0)=1, where S(n,k) = 2*A340106(n-1,k-1) - 2*A340106(n-2,k-2) + S(n-3,k-3), S(n,k)=0 for k <= 0. [exception added by Xiangyu Chen, Aug 19 2022]
EXAMPLE
n\k 0 1 2 3 4 5 6 7 8
0 1
1 1 1
2 1 2 2
3 1 3 6 0
4 1 4 12 16 16
5 1 5 20 50 90 80
6 1 6 30 108 300 552 516
7 1 7 42 196 742 2100 3990 3794
8 1 8 56 320 1536 5888 16976 32656 31456
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Xiangyu Chen, Dec 28 2020
STATUS
approved