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%I #13 Jan 27 2024 14:24:51
%S 0,0,0,2,6,40,238,1760,14076,131732,1308670,14678452,176166906,
%T 2317481348,32416648496,490915956484,7846449011500,134291298372632,
%U 2416652824505150,46141903780094080,922528719841017424,19456439433050482412,427837767407051523776,9873256397944571377332
%N Number of permutations of {1..n} with three consecutive terms in arithmetic progression.
%C Also permutations whose second differences have at least one zero.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Arithmetic_progression">Arithmetic progression</a>
%F a(n) = n! - A295370(n).
%e The a(3) = 2 and a(4) = 6 permutations:
%e (1,2,3) (1,2,3,4)
%e (3,2,1) (1,4,3,2)
%e (2,3,4,1)
%e (3,2,1,4)
%e (4,1,2,3)
%e (4,3,2,1)
%t Table[Select[Permutations[Range[n]],MatchQ[Differences[#],{___,x_,x_,___}]&]//Length,{n,0,8}]
%Y The complement is counted by A295370.
%Y The version for prime indices is A333195.
%Y Strict partitions with equal differences are A049980.
%Y Partitions with equal differences are A049988.
%Y Compositions without triples in arithmetic progression are A238423.
%Y Partitions without triples in arithmetic progression are A238424.
%Y Strict partitions without triples in arithmetic progression are A332668.
%Y Cf. A000142, A007862, A175342, A325849, A325850.
%K nonn
%O 0,4
%A _Gus Wiseman_, Mar 31 2020
%E a(11)-a(21) (using A295370) from _Giovanni Resta_, Apr 07 2020
%E a(22)-a(23) (using A295370) from _Alois P. Heinz_, Jan 27 2024
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