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, except side (1,n) is unrestricted.
FORMULA
T(n,k) = A340107(n,k) + 2*O(n-1,k-1) + O(n-2,k-2), where O(n,k) = 2*(k-1)*T(n-1,k-1)/(n-1) - 2*O(n-1,k-1) + 3*O(n-2,k-2) + 2*O(n-3,k-3) + O(n-4,k-4), O(n,k)=0 for k<=1.
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 4
4 1 4 12 20 18
5 1 5 20 54 100 92
6 1 6 30 112 318 600 570
7 1 7 42 200 768 2208 4244 4082
8 1 8 56 324 1570 6080 17682 34300 33292
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Xiangyu Chen, Dec 28 2020
STATUS
approved