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A184965 Number of permutations p of [n] such that (n-p(i)+i) mod n >= 6 for all i.

%I A184965 #29 Oct 25 2023 16:19:18
%S A184965 1,0,0,0,0,0,0,1,2,78,888,13909,204448,3182225,51504968,873224962,
%T A184965 15498424578,287972983669,5598118158336,113756109812283,
%U A184965 2413723031593090,53416658591208438,1231458960862452472,29538634475147637783,736321207493996695072
%N A184965 Number of permutations p of [n] such that (n-p(i)+i) mod n >= 6 for all i.
%H A184965 Shalosh B. Ekhad and Doron Zeilberger, <a href="/A184965/b184965.txt">Table of n, a(n) for n = 0..100</a>
%H A184965 D. Zeilberger, <a href="http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/menages.html">Automatic Enumeration of Generalized Ménage Numbers</a>
%e A184965 a(8) = 2: (2,3,4,5,6,7,8,1), (3,4,5,6,7,8,1,2).
%p A184965 with(LinearAlgebra):
%p A184965 a:= n-> `if`(n=0, 1, Permanent(Matrix(n, (i, j)->
%p A184965                      `if`(i-j<=0 and i-j>-6 or i-j>n-6, 0, 1)))):
%p A184965 seq(a(n), n=0..15);
%t A184965 a[n_] := Permanent[Table[If[i-j <= 0 && i-j > -6 || i-j > n-6, 0, 1], {i, 1, n}, {j, 1, n}]]; a[0] = 1; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 15}] (* _Jean-François Alcover_, Jan 07 2016, adapted from Maple *)
%Y A184965 A diagonal of A008305.
%Y A184965 Cf. A000142, A000166, A000179, A000183, A004307.
%K A184965 nonn
%O A184965 0,9
%A A184965 _Alois P. Heinz_, Apr 20 2011