A324373 Number of permutations p of [n] whose absolute displacements |p(i)-i| are Fibonacci numbers.

1, 1, 2, 6, 24, 78, 362, 1473, 5657, 30045, 150862, 690604, 3048236, 14043152, 84667280, 484698208, 2661357616, 13753927840, 73080151824, 374413073328, 1963753297884, 10358706625196, 69857764331270, 447802562823975

Offset

0,3

Links

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

Wikipedia, Permutation

Maple

g:= proc(n) g(n):= (t-> issqr(t+4) or issqr(t-4))(5*n^2) end:
b:= proc(s) option remember; (n-> `if`(n=0, 1, add(`if`(
       g(abs(n-j)), b(s minus {j}), 0), j=s)))(nops(s))
    end:
a:= n-> b({$1..n}):
seq(a(n), n=0..16);

Mathematica

g[n_] := With[{t = 5 n^2}, IntegerQ@Sqrt[t + 4] || IntegerQ@Sqrt[t - 4]];
b[s_] := b[s] = With[{n = Length[s]}, If[n == 0, 1, Sum[If[g[Abs[n - j]], b[s ~Complement~ {j}], 0], {j, s}]]];
a[n_] :=  b[Range[n]];
a /@ Range[0, 16] (* Jean-François Alcover, Mar 25 2021, after Alois P. Heinz *)

Crossrefs

Cf. A000045, A000142, A324372, A324374, A324375, A324376.

Sequence in context: A263698 A263747 A002526 * A117665 A068777 A372854

Adjacent sequences: A324370 A324371 A324372 * A324374 A324375 A324376

Keyword

nonn

Author

Alois P. Heinz, Feb 25 2019

Status

approved