A324374 Number of permutations p of [n] whose absolute displacements |p(i)-i| are triangular numbers.

1, 1, 2, 3, 9, 19, 49, 173, 542, 1811, 5061, 23744, 93973, 385493, 1394506, 5342437, 29798445, 138233786, 689926740, 3068163126, 14882203929, 67731732263, 412791651318, 2341487404144, 13639722130984

Offset

0,3

Links

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

Wikipedia, Permutation

Example

a(3) = 3: 123, 132, 213.
a(4) = 9: 1234, 1243, 1324, 2134, 2143, 2341, 4123, 4231, 4321.
a(5) = 19: 12345, 12354, 12435, 13245, 13254, 13452, 15234, 15342, 15432, 21345, 21354, 21435, 23415, 25314, 41235, 41352, 42315, 43215, 45312.

Maple

g:= proc(n) option remember; issqr(8*n+1) 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_] := g[n] = IntegerQ@Sqrt[8n+1];
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. A000142, A000217, A324372, A324373, A324375, A324376.

Sequence in context: A094812 A307898 A079992 * A106519 A006866 A121908

Adjacent sequences: A324371 A324372 A324373 * A324375 A324376 A324377

Keyword

nonn

Author

Alois P. Heinz, Feb 25 2019

Status

approved