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A295370 Number of permutations of [n] avoiding three consecutive terms in arithmetic progression. 16
1, 1, 2, 4, 18, 80, 482, 3280, 26244, 231148, 2320130, 25238348, 302834694, 3909539452, 54761642704, 816758411516, 13076340876500, 221396129723368, 3985720881222850, 75503196628737920, 1510373288335622576, 31634502738658957588, 696162960370556156224, 15978760340940405262668 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
These are permutations of n whose second-differences are nonzero. - Gus Wiseman, Jun 03 2019
LINKS
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.
Sequence in context: A295767 A318230 A075836 * A292280 A120664 A095816
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 20 2017
EXTENSIONS
a(22)-a(23) from Vaclav Kotesovec, Mar 22 2022
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)