A257953 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).

1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496, 1334961, 14684570, 176214841, 2290792932, 32071101049, 481066515734, 7697064251745, 130850092279664, 2355301661033953, 44750731559645106, 312426715251262464, 2178674876680100744, 15178362413058474596, 105663183116236278362

Offset

0,4

Comments

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

Links

Table of n, a(n) for n=0..23.

Maple

a:= n-> `if`(n=0, 1, LinearAlgebra[Permanent](Matrix(n, (i, j)->
        `if`(i<>j and (i-j mod n<=9 or j-i mod n<=9), 1, 0)))):
seq(a(n), n=0..20);

Mathematica

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 *)

Crossrefs

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

Cf. A259782.

Sequence in context: A260111 A260091 A260115 * A260216 A182386 A000166

Adjacent sequences: A257950 A257951 A257952 * A257954 A257955 A257956

Keyword

nonn

Author

Alois P. Heinz, Jul 19 2015

Status

approved