A381461 Number of permutations of [n] with no fixed points where adjacent elements differ by at least 3.

1, 0, 0, 0, 0, 0, 2, 8, 115, 1274, 15099, 179628, 2260064, 30534802, 441269110, 6789665680, 110947884520, 1920180939650, 35099424286573, 675866037989156, 13676799446869485, 290208293166279344, 6443880771921767240

Offset

0,7

Links

Table of n, a(n) for n=0..22.

Robert P. P. McKone, The permutations n=6 to n=11.

Wikipedia, Permutation

Example

a(6) = 2: 362514, 415263.
a(7) = 8: 2516374, 3615274, 3625174, 3627415, 3741625, 4152736, 4163725, 4173625.
a(8) = 115: 25163847, 25174836, 25184736, 25814736, ..., 84736251, 85263714, 85263741, 85274163.

Maple

b:= proc(s, l) option remember; (n-> `if`(n=0, 1, add(
     `if`(j=n or abs(l-j)<3, 0, b(s minus {j}, j)), j=s)))(nops(s))
    end:
a:= n-> b({$1..n}, -2):
seq(a(n), n=0..16);

Mathematica

Clear[permCount]; permCount[s_, last_] := permCount[s, last] = Module[{n, j}, n = Length[s]; If[n == 0, 1, Total[Table[If[j == n || Abs[last - j] < 3, 0, permCount[Complement[s, {j}], j]], {j, s}]]]]; Table[permCount[Range[n], -2], {n, 0, 12}] (* Robert P. P. McKone, Mar 01 2025 *)

Crossrefs

Cf. A000166, A002464, A127697, A288208.

Sequence in context: A263249 A297631 A374380 * A099292 A284967 A064111

Adjacent sequences: A381458 A381459 A381460 * A381462 A381463 A381464

Keyword

nonn,more

Author

Alois P. Heinz, Feb 24 2025

Status

approved