A260091 Number of permutations p of [n] with no fixed points and cyclic displacement of elements restricted by seven: p(i)<>i and (i-p(i) mod n <= 7 or p(i)-i mod n <= 7).

1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496, 1334961, 14684570, 176214841, 2290792932, 32071101049, 481066515734, 2649865335040, 14570246018686, 80002336342276, 438791546196382, 2404416711392528, 13164695578635648, 72030936564665508, 393911127182051942

Offset

0,4

Comments

a(n) = A000166(n) for n <= 15.

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<=7 or j-i mod n<=7), 1, 0)))):
seq(a(n), n=0..16);

Mathematica

a[n_] := If[n == 0, 1, Permanent[Table[If[i != j && (Mod[i - j, n] <= 7 || Mod[j - i, n] <= 7), 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 *)

Crossrefs

Cf. A000166, A260074, A260081, A260092, A260094, A260111, A260115, A257953, A260216.

Cf. A259780.

Sequence in context: A260094 A259783 A260111 * A260115 A257953 A260216

Adjacent sequences: A260088 A260089 A260090 * A260092 A260093 A260094

Keyword

nonn

Author

Alois P. Heinz, Jul 16 2015

Status

approved