A075852 Number of permutations s of {1,2,...,n} such that |s(i)-i|>3 for each i=1,2,...,n.

1, 0, 0, 0, 0, 0, 0, 0, 1, 16, 436, 6984, 114124, 1799688, 29125117, 486980182, 8490078104, 154750897552, 2951968964768, 58917663227568, 1229367602071416, 26787823838035750, 608794318333169289, 14411810690642972432

Offset

0,10

Comments

a(n) equals the permanent of the n X n matrix with 0's along the main diagonal, the subdiagonal, the superdiagonal, the sub-subdiagonal, the super-superdiagonal, the sub-sub-subdiagonal, the super-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

George Spahn and Doron Zeilberger, Automatic Counting of Generalized Latin Rectangles and Trapezoids, arXiv:2108.11285 [math.CO], 2021.

Maple

b:= proc(s) option remember; (n-> `if`(n=0, 1, add(
      `if`(abs(n-i)>3, 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 < 8, 0, SparseArray[{Band[{1, 1}] -> 0, Band[{2, 1}] -> 0, Band[{3, 1}] -> 0, Band[{4, 1}] -> 0, Band[{1, 2}] -> 0, Band[{1, 3}] -> 0, Band[{1, 4}] -> 0}, {n, n}, 1] // Permanent];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 23}] (* Jean-François Alcover, May 01 2019 *)

Crossrefs

Cf. A001883, A075851.

Sequence in context: A118994 A223686 A000489 * A260853 A068792 A229583

Adjacent sequences: A075849 A075850 A075851 * A075853 A075854 A075855

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