A084894 Number of permutations of length n such that at least one absolute difference between consecutive elements has a distinct partner.

0, 0, 2, 20, 112, 696, 5008, 40280, 362760, 3628504, 39916152, 479000272, 6227017600, 87178281288, 1307674342408, 20922789832080, 355687427952808, 6402373705217304, 121645100407380704, 2432902008173142656, 51090942171698988176, 1124000727777569109296

Offset: 1

Author

Jon Perry, Jun 10 2003

Keywords

• nonn

Examples

			a(3)=2 as only 123 and 321 have the required property, with differences of 1,1. The rest all have differences of 1,2.
		

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..40

Crossrefs

Cf. A000142, A006967.

Programs

Mathematica

A006967 = Cases[Import["https://oeis.org/A006967/b006967.txt", "Table"], {, }][[All, 2]];
a[n_] := n! - A006967[[n+1]];
a /@ Range[40] (* Jean-François Alcover, Jan 31 2020 *)

PARI

{ for (n=3,10,x=vector(n-1); s=0; for (i=1,n!,v=numtoperm(n,i); for (j=1,n-1,x[j]=abs(v[j+1]-v[j])); x=vecsort(x); fl=0; for (k=1,n-2,if (x[k]==x[k+1],fl=1; break)); if (fl==1,s++)); print(n"; "s)) }

Formula

a(n) = n! - A006967(n).