A295370 Number of permutations of [n] avoiding three consecutive terms in arithmetic progression.

1, 1, 2, 4, 18, 80, 482, 3280, 26244, 231148, 2320130, 25238348, 302834694, 3909539452, 54761642704, 816758411516, 13076340876500, 221396129723368, 3985720881222850, 75503196628737920, 1510373288335622576, 31634502738658957588, 696162960370556156224, 15978760340940405262668

Offset

0,3

Comments

These are permutations of n whose second-differences are nonzero. - Gus Wiseman, Jun 03 2019

Links

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

Wikipedia, Arithmetic progression

Index entries related to non-averaging sequences

Example

a(3) = 4: 132, 213, 231, 312.
a(4) = 18: 1243, 1324, 1342, 1423, 2134, 2143, 2314, 2413, 2431, 3124, 3142, 3241, 3412, 3421, 4132, 4213, 4231, 4312.

Maple

b:= proc(s, j, k) option remember; `if`(s={}, 1,
      add(`if`(k=0 or 2*j<>i+k, b(s minus {i}, i,
          `if`(2*i-j in s, j, 0)), 0), i=s))
    end:
a:= n-> b({$1..n}, 0$2):
seq(a(n), n=0..12);

Mathematica

Table[Length[Select[Permutations[Range[n]], !MemberQ[Differences[#, 2], 0]&]], {n, 0, 5}] (* Gus Wiseman, Jun 03 2019 *)
b[s_, j_, k_] := b[s, j, k] = If[s == {}, 1, Sum[If[k == 0 || 2*j != i + k, b[s~Complement~{i}, i, If[MemberQ[s, 2*i - j ], j, 0]], 0], {i, s}]];
a[n_] := a[n] = b[Range[n], 0, 0];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 16}] (* Jean-François Alcover, Nov 20 2023, after Alois P. Heinz *)

Crossrefs

Column k=0 of A295390.

Cf. A003407, A174080, A238423, A238424, A338765.

Cf. A049988, A175342, A279945, A325545, A325849, A325850, A325851, A325874, A325875.

Sequence in context: A295767 A318230 A075836 * A292280 A120664 A095816

Adjacent sequences: A295367 A295368 A295369 * A295371 A295372 A295373

Keyword

nonn

Author

Alois P. Heinz, Nov 20 2017

Extensions

a(22)-a(23) from Vaclav Kotesovec, Mar 22 2022

Status

approved