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A260092
Number of permutations p of [n] with no fixed points and cyclic displacement of elements restricted by four: p(i)<>i and (i-p(i) mod n <= 4 or p(i)-i mod n <= 4).
9
1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496, 440192, 1445100, 4728000, 15405008, 49955280, 162442816, 530284304, 1738077424, 5714461760, 18795784436, 61868602624, 203858323008, 672535917712, 2221505855492, 7345985276816, 24314075406208, 80542683435168
OFFSET
0,4
COMMENTS
a(n) = A000166(n) for n <= 9.
MAPLE
a:= n-> `if`(n=0, 1, LinearAlgebra[Permanent](Matrix(n, (i, j)->
`if`(i<>j and (i-j mod n<=4 or j-i mod n<=4), 1, 0)))):
seq(a(n), n=0..15);
MATHEMATICA
a[n_] := If[n == 0, 1, Permanent[Table[If[i != j && (Mod[i - j, n] <= 4 || Mod[j - i, n] <= 4), 1, 0], {i, 1, n}, {j, 1, n}]]]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 15}] (* Jean-François Alcover, Jan 06 2016, adapted from Maple *)
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 15 2015
STATUS
approved