A324375 Number of permutations p of [n] whose absolute displacements |p(i)-i| are square numbers.

1, 1, 2, 3, 5, 13, 29, 68, 165, 339, 1249, 3706, 11749, 39151, 105714, 321361, 938529, 4112583, 16778058, 64073812, 260625900, 917269164, 3451696842, 13068376545, 48655092849

Offset

0,3

Links

Table of n, a(n) for n=0..24.

Wikipedia, Permutation

Example

a(3) = 3: 123, 132, 213.
a(4) = 5: 1234, 1243, 1324, 2134, 2143.
a(5) = 13: 12345, 12354, 12435, 13245, 13254, 21345, 21354, 21435, 23451, 51234, 52341, 52431, 53241.

Maple

b:= proc(s) option remember; (n-> `if`(n=0, 1, add(`if`(
     issqr(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

b[s_] := b[s] = Function[n, If[n == 0, 1, Sum[If[IntegerQ@Sqrt[Abs[n-j]], b[s ~Complement~ {j}], 0], {j, s}]]][Length[s]];
a[n_] := b[Range[n]];
a /@ Range[0, 16] (* Jean-François Alcover, Apr 23 2021, after Alois P. Heinz *)

Crossrefs

Cf. A000142, A000290, A324372, A324373, A324374, A324376.

Sequence in context: A072536 A087592 A248526 * A038879 A162390 A108515

Adjacent sequences: A324372 A324373 A324374 * A324376 A324377 A324378

Keyword

nonn

Author

Alois P. Heinz, Feb 25 2019

Status

approved