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%I #9 Apr 17 2021 08:34:01
%S 1,1,2,6,24,108,632,4408,35336,319056,3205824,35451984,427683560,
%T 5588310904,78615281768,1184587864512,19033796498496,324852522308160,
%U 5868833343451592,111889157407344424
%N Number of permutations of length n with no consecutive triples i,i+2,i+4 or i,i-2,i-4.
%C Note for n<5 there are no such subsequences, so those values are trivially n!. Also note it is possible for a permutation to have both i,i+2,i+4 and i,i-2,i-4 triples, as in an example from n=7: (2,4,6,5,3,1,0). This permutation is not counted by a(7).
%e For n=5 there are 5!-a(5)=12 permutations with i,i+2,i+4 or i,i-2,i-4 triples. An examples of one is (4,2,0,1,3).
%Y Cf. A095816, A174077, A174078, A174079.
%K nonn,more
%O 0,3
%A _Isaac Lambert_, Mar 10 2010
%E a(0)-a(4) and a(10)-a(19) from _Alois P. Heinz_, Apr 14 2021