A075851 Number of permutations s of {1,2,...,n} such that |s(i)-i|>2 for each i=1,2,...,n.

1, 0, 0, 0, 0, 0, 1, 8, 112, 1168, 13365, 159414, 2036488, 27780408, 404351752, 6263006598, 102946702825, 1790795492176, 32880327473840, 635630231970048, 12907624693811937, 274744151265431700, 6117666413618771968, 142238172767973342656

Offset: 0

Author

Reiner Martin, Oct 15 2002

Keywords

• nonn

Comments

a(n) equals the permanent of the n X n matrix with 0's along the main diagonal, the superdiagonal, the subdiagonal, the sub-subdiagonal, the super-superdiagonal, and 1's everywhere else. - John M. Campbell, Jul 09 2011

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..450

Crossrefs

Cf. A001883, A075852.

Programs

Maple

b:= proc(s) option remember; (n-> `if`(n=0, 1, add(
      `if`(abs(n-i)>2, b(s minus {i}), 0), i=s)))(nops(s))
    end:
a:= n-> b({$1..n}):
seq(a(n), n=0..15);  # Alois P. Heinz, Jan 25 2019

Mathematica

a[0] = 1; a[n_] := a[n] = If[n<6, 0, SparseArray[{Band[{1, 1}] -> 0, Band[{2, 1}] -> 0, Band[{3, 1}] -> 0, Band[{1, 2}] -> 0, Band[{1, 3}] -> 0}, {n, n}, 1] // Permanent];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 23}] (* Jean-François Alcover, Apr 30 2019 *)

Extensions

More terms from Vladimir Baltic, Vladeta Jovovic, Jan 04 2003

a(21) from Alois P. Heinz, Jul 04 2015

a(22)-a(23) from Alois P. Heinz, Jan 22 2019

a(0)=1 prepended by Alois P. Heinz, Jan 25 2019