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 A232864 Number of permutations of n elements not cyclically containing the consecutive pattern 123. 2
 1, 1, 2, 3, 12, 45, 234, 1323, 8856, 65529, 543510, 4937031, 49030596, 526930677, 6101871426, 75686176035, 1001517264432, 14079895613937, 209594037600558, 3293305758743679, 54470994630103260, 945988795762018029, 17211193919411902938, 327371367293394753627 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..200 R. Ehrenborg, Cyclically consecutive permutation avoidance, arXiv:1312.2051 [math.CO], 2013 FORMULA a(n) = n! * Sum_{k=-oo..oo} (sqrt(3)/(2*Pi*(k+1/3)))^n for n >= 2. a(n) = A080635(n-1)*n for n>0. - Alois P. Heinz, Dec 01 2013 EXAMPLE For n=4 the a(4) = 12 comes from the 3 permutations 1324, 1423 and 1432; and by cyclically shifting we obtain 3 * 4 = 12 permutations. MAPLE b:= proc(u, o, t) option remember; `if`(u+o=0, 1, `if`(t<2, add(b(u+j-1, o-j, t+1), j=1..o), 0)+ add(b(u-j, o+j-1, 1), j=1..u)) end: a:= n-> `if`(n=0, 1, n*b(0, n-1, 1)): seq(a(n), n=0..25); # Alois P. Heinz, Dec 01 2013 MATHEMATICA b[u_, o_, t_] := b[u, o, t] = If[u+o==0, 1, If[t<2, Sum[b[u+j-1, o-j, t+1], {j, 1, o}], 0] + Sum[b[u-j, o+j-1, 1], {j, 1, u}]]; a[n_]:= If[n==0, 1, n*b[0, n-1, 1]]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Aug 14 2017, after Alois P. Heinz *) CROSSREFS Cf. A049774, A080635. Sequence in context: A012306 A012312 A009243 * A307957 A307956 A358716 Adjacent sequences: A232861 A232862 A232863 * A232865 A232866 A232867 KEYWORD nonn AUTHOR Richard Ehrenborg, Dec 01 2013 STATUS approved

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Last modified March 24 09:16 EDT 2023. Contains 361470 sequences. (Running on oeis4.)