A091217 Number of permutations p of [n] such that the n-1 sums p(i)+p(i+1) (i=1,2,...n-1) are all distinct.

1, 1, 2, 6, 16, 54, 232, 1132, 6024, 36262, 242080, 1775316, 14135584, 122077832, 1131066448, 11230979624, 118638940864

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Example

For a(4), we have 2+3=1+4, so a(4)=4! - (23)(14) - (14)(32) = 24 - 4 - 4 = 16.
For a(5), we have 1+4=2+3, 1+5=2+4, 2+5=3+4 to avoid.

Prog

(PARI) { for (i=3, 9, v=vector(i-1); c=0; for (j=1, i!, x=numtoperm(i, j); for (k=1, i-1, v[k]=x[k]+x[k+1]); fl=0; v=vecsort(v); for (z=1, i-2, if (v[z]==v[z+1], fl=1; break)); if (fl==0, c++)); print1(", "c)) }

Crossrefs

Sequence in context: A147949 A147940 A147931 * A147891 A147922 A147913

Adjacent sequences: A091214 A091215 A091216 * A091218 A091219 A091220

Keyword

hard,more,nonn

Author

Jon Perry, Feb 23 2004

Extensions

a(10)-a(11) from John W. Layman, Mar 10 2004

More terms from R. H. Hardin, Nov 11 2008

Definition corrected by Emeric Deutsch, Nov 28 2008

a(0)=1 prepended by Alois P. Heinz, Jul 06 2021

Status

approved