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%I #19 Jan 05 2019 01:35:23
%S 0,0,0,0,2,4,22,124,816,6112,51642,485604,5034606,57080204,702766384,
%T 9339630016,133281949954,2033044422948,33014191980502,568686463073484,
%U 10357838456504880
%N Number of circular permutations with exactly one specified increasing or decreasing modular run (3-sequence), with clockwise and counterclockwise traversals counted as distinct.
%D Paul J. Campbell, Circular permutations with exactly one modular run (3-sequence), submitted to Journal of Integer Sequences
%H Wayne M. Dymáček and Isaac Lambert, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL14/Dymacek/dymacek5.html">Circular permutations avoiding runs of i, i+1, i+2 or i, i-1, i-2</a>, Journal of Integer Sequences, Vol. 14 (2011) Article 11.1.6.
%F a(n) = 2*A235937(n).
%e With specified sequence 123:
%e a(5) = 2: 12354, 32154.
%e a(6) = 4: 123564, 321564, 123645, 321546.
%Y Cf. A165961, A165964, A165962, A078628, A078673.
%Y Cf. A235937, A235939, A235940, A235941, A235942, A235943.
%K nonn
%O 1,5
%A _Paul J. Campbell_, Jan 20 2014, with Joe Marasco and Ashish Vikram
%E a(20)-a(21) from _Alois P. Heinz_, Jan 24 2014
%E Obsolete b-file deleted by _N. J. A. Sloane_, Jan 05 2019