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A333631
Number of permutations of {1..n} with three consecutive terms in arithmetic progression.
1
0, 0, 0, 2, 6, 40, 238, 1760, 14076, 131732, 1308670, 14678452, 176166906, 2317481348, 32416648496, 490915956484, 7846449011500, 134291298372632, 2416652824505150, 46141903780094080, 922528719841017424, 19456439433050482412, 427837767407051523776, 9873256397944571377332
OFFSET
0,4
COMMENTS
Also permutations whose second differences have at least one zero.
FORMULA
a(n) = n! - A295370(n).
EXAMPLE
The a(3) = 2 and a(4) = 6 permutations:
(1,2,3) (1,2,3,4)
(3,2,1) (1,4,3,2)
(2,3,4,1)
(3,2,1,4)
(4,1,2,3)
(4,3,2,1)
MATHEMATICA
Table[Select[Permutations[Range[n]], MatchQ[Differences[#], {___, x_, x_, ___}]&]//Length, {n, 0, 8}]
CROSSREFS
The complement is counted by A295370.
The version for prime indices is A333195.
Strict partitions with equal differences are A049980.
Partitions with equal differences are A049988.
Compositions without triples in arithmetic progression are A238423.
Partitions without triples in arithmetic progression are A238424.
Strict partitions without triples in arithmetic progression are A332668.
Sequence in context: A350971 A119692 A264152 * A337071 A354313 A351739
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 31 2020
EXTENSIONS
a(11)-a(21) (using A295370) from Giovanni Resta, Apr 07 2020
a(22)-a(23) (using A295370) from Alois P. Heinz, Jan 27 2024
STATUS
approved