A257953 - OEIS

%I #44 Jan 06 2016 12:09:43

%S 1,0,1,2,9,44,265,1854,14833,133496,1334961,14684570,176214841,

%T 2290792932,32071101049,481066515734,7697064251745,130850092279664,

%U 2355301661033953,44750731559645106,312426715251262464,2178674876680100744,15178362413058474596,105663183116236278362

%N Number of permutations p of [n] with no fixed points and cyclic displacement of elements restricted by nine: p(i)<>i and (i-p(i) mod n <= 9 or p(i)-i mod n <= 9).

%C a(n) = A000166(n) for n <= 19.

%p a:= n-> `if`(n=0, 1, LinearAlgebra[Permanent](Matrix(n, (i, j)->

%p         `if`(i<>j and (i-j mod n<=9 or j-i mod n<=9), 1, 0)))):

%p seq(a(n), n=0..20);

%t a[n_] := If[n == 0, 1, Permanent[Table[If[i != j && (Mod[i - j, n] <= 9 || Mod[j - i, n] <= 9), 1, 0], {i, 1, n}, {j, 1, n}]]]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 20}] (* _Jean-François Alcover_, Jan 06 2016, adapted from Maple *)

%Y Cf. A000166, A260074, A260081, A260092, A260094, A260111, A260091, A260115, A260216.

%Y Cf. A259782.

%K nonn

%O 0,4

%A _Alois P. Heinz_, Jul 19 2015