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A260111
Number of permutations p of [n] with no fixed points and cyclic displacement of elements restricted by six: p(i)<>i and (i-p(i) mod n <= 6 or p(i)-i mod n <= 6).
9
1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496, 1334961, 14684570, 176214841, 2290792932, 10930514688, 52034548064, 247272708868, 1173385630596, 5560837425792, 26322368822528, 124470922522980, 589274182149120, 2793967092494408, 13269446868206480, 63125696320334912
OFFSET
0,4
COMMENTS
a(n) = A000166(n) for n <= 13.
MAPLE
a:= n-> `if`(n=0, 1, LinearAlgebra[Permanent](Matrix(n, (i, j)->
`if`(i<>j and (i-j mod n<=6 or j-i mod n<=6), 1, 0)))):
seq(a(n), n=0..16);
MATHEMATICA
a[n_] := If[n == 0, 1, Permanent[Table[If[i != j && (Mod[i - j, n] <= 6 || Mod[j - i, n] <= 6), 1, 0], {i, 1, n}, {j, 1, n}]]]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 16}] (* Jean-François Alcover, Jan 06 2016, adapted from Maple *)
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 16 2015
STATUS
approved