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A075851
Number of permutations s of {1,2,...,n} such that |s(i)-i|>2 for each i=1,2,...,n.
8
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
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
Sequence in context: A317000 A316818 A317568 * A270111 A053536 A139741
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