A260115 Number of permutations p of [n] with no fixed points and cyclic displacement of elements restricted by eight: p(i)<>i and (i-p(i) mod n <= 8 or p(i)-i mod n <= 8).

1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496, 1334961, 14684570, 176214841, 2290792932, 32071101049, 481066515734, 7697064251745, 130850092279664, 817154768973824, 5095853023109484, 31742020729513344, 197541094675490640, 1228455950686697872, 7634711586761705092

Offset

0,4

Comments

a(n) = A000166(n) for n <= 17.

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<=8 or j-i mod n<=8), 1, 0)))):
seq(a(n), n=0..18);

Mathematica

a[n_] := If[n == 0, 1, Permanent[Table[If[i != j && (Mod[i - j, n] <= 8 || Mod[j - i, n] <= 8), 1, 0], {i, 1, n}, {j, 1, n}]]]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 18}] (* Jean-François Alcover, Jan 06 2016, adapted from Maple *)

Crossrefs

Cf. A000166, A260074, A260081, A260092, A260094, A260111, A260091, A257953, A260216.

Cf. A259781.

Sequence in context: A259783 A260111 A260091 * A257953 A260216 A182386

Adjacent sequences: A260112 A260113 A260114 * A260116 A260117 A260118

Keyword

nonn

Author

Alois P. Heinz, Jul 16 2015

Status

approved