OFFSET
2,4
COMMENTS
The 12th row of the triangle given in the Sade reference is incorrect, since the first column of this triangle is known (it is A000560).
REFERENCES
A. Sade, Sur les Chevauchements des Permutations, published by the author, Marseille, 1949
LINKS
Albert Sade, Sur les Chevauchements des Permutations, published by the author, Marseille, 1949. [Annotated scanned copy]
EXAMPLE
Triangle begins:
0;
1, 0;
2, 0, 0;
5, 0, 1, 0;
12, 0, 2, 0, 0;
33, 1, 7, 0, 1, 0;
87, 2, 17, 0, 2, 0, 0;
252, 11, 55, 2, 9, 0, 1, 0;
703, 26, 145, 4, 22, 0, 2, 0, 0;
2105, 109, 467, 27, 81, 3, 11, 0, 1, 0;
...
PROG
(PARI)
Overlapfree(v)={for(i=1, #v, for(j=i+1, v[i]-1, if(v[j]>v[i], return(0)))); 1}
Chords(u)={my(n=2*#u, v=vector(n), s=u[#u]); if(s%2==0, s=n+1-s); for(i=1, #u, my(t=n+1-s); s=u[i]; if(s%2==0, s=n+1-s); v[s]=t; v[t]=s); v}
FirstRunLen(v)={my(e=1); for(i=1, #v, if(v[i]==e, e++)); e-2}
row(n)={my(r=vector(n-1)); if(n>=2, forperm(n, v, if(v[1]<>1, break); if(v[2]<>2 && Overlapfree(Chords(v)), r[FirstRunLen(v)]++))); r}
for(n=2, 8, print(row(n))) \\ Andrew Howroyd, Dec 07 2018
CROSSREFS
KEYWORD
AUTHOR
N. J. A. Sloane, Jul 05 2015
EXTENSIONS
a(49) corrected and a(57)-a(67) from Andrew Howroyd, Dec 07 2018
STATUS
approved