OFFSET
0,5
COMMENTS
In a convex n-gon, the number of paths using k-1 diagonals and k non-repeated vertices.
FORMULA
EXAMPLE
n\k 0 1 2 3 4 5 6 7 8
0 1
1 1 1
2 1 2 0
3 1 3 0 0
4 1 4 4 0 0
5 1 5 10 10 10 10
6 1 6 18 36 60 84 60
7 1 7 28 84 210 434 630 462
8 1 8 40 160 544 1552 3440 5168 3920
PROG
(PARI) isokd(d, n) = my(x=abs(d)); (x==1) || (x==(n-1));
isok(s, p, n) = {my(w = vector(#s, k, s[p[k]])); for (i=1, #s-1, if (isokd(w[i+1] - w[i], n) == 1, return (0))); return (1); }
T(n, k) = {my(nb = 0); forsubset([n, k], s, for(i=1, k!, if (isok(s, numtoperm(k, i), n), nb++); ); ); nb; } \\ Michel Marcus, Nov 21 2020
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Xiangyu Chen, Nov 11 2020
STATUS
approved