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

0,8

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

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 *)

Crossrefs

Cf. A001883, A075852.

Sequence in context: A317000 A316818 A317568 * A270111 A053536 A139741

Adjacent sequences: A075848 A075849 A075850 * A075852 A075853 A075854

Keyword

nonn

Author

Reiner Martin, Oct 15 2002

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

Status

approved