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%I A219587 #24 Jun 22 2019 09:23:55
%S A219587 1,2,8,40,224,1296,7568,44304,259536,1520656,8910160,52209040,
%T A219587 305919696,1792542992,10503446608,61545189520,360625475024,
%U A219587 2113093401616,12381720203088,72550979111824,425114158957776,2490966357221136,14595875630354000,85524874633320080
%N A219587 Noncrossing, nonnesting, 2-arc-colored permutations on the set {1..n} where lower arcs even of different colors do not cross.
%C A219587 The sequence is generated by a rational function, in particular, a quotient of two determinants.
%H A219587 Lily Yen, <a href="/A219587/b219587.txt">Table of n, a(n) for n = 0..1000</a>
%H A219587 Lily Yen, <a href="http://arxiv.org/abs/1211.3472">Crossings and Nestings for Arc-Coloured Permutations</a>, arXiv:1211.3472 [math.CO], 2012-2013.
%H A219587 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-6,-4).
%F A219587 G.f.: (1 - 5*x)/(1 - 7*x + 6*x^2 + 4*x^3).
%F A219587 a(n) = 7*a(n-1) - 6*a(n-2) - 4*a(n-3) for n>2. - _Colin Barker_, Jun 22 2019
%e A219587 For n=4, the a(4) = 224 solutions are 24 permutations, 8 of which can be colored in 4 ways each, 8 in 8 ways each, and 8 in 16 ways each, thus resulting in 8 * (4+8+16) = 224.
%o A219587 (PARI) Vec((1 - 5*x) / (1 - 7*x + 6*x^2 + 4*x^3) + O(x^40)) \\ _Colin Barker_, Jun 22 2019
%K A219587 nonn,easy
%O A219587 0,2
%A A219587 _Lily Yen_, Nov 23 2012
%E A219587 Name modified by _Lily Yen_, Apr 23 2013

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