A219587 - OEIS

%I #24 Jun 22 2019 09:23:55

%S 1,2,8,40,224,1296,7568,44304,259536,1520656,8910160,52209040,

%T 305919696,1792542992,10503446608,61545189520,360625475024,

%U 2113093401616,12381720203088,72550979111824,425114158957776,2490966357221136,14595875630354000,85524874633320080

%N Noncrossing, nonnesting, 2-arc-colored permutations on the set {1..n} where lower arcs even of different colors do not cross.

%C The sequence is generated by a rational function, in particular, a quotient of two determinants.

%H Lily Yen, <a href="/A219587/b219587.txt">Table of n, a(n) for n = 0..1000</a>

%H 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 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-6,-4).

%F G.f.: (1 - 5*x)/(1 - 7*x + 6*x^2 + 4*x^3).

%F a(n) = 7*a(n-1) - 6*a(n-2) - 4*a(n-3) for n>2. - _Colin Barker_, Jun 22 2019

%e 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 (PARI) Vec((1 - 5*x) / (1 - 7*x + 6*x^2 + 4*x^3) + O(x^40)) \\ _Colin Barker_, Jun 22 2019

%K nonn,easy

%O 0,2

%A _Lily Yen_, Nov 23 2012

%E Name modified by _Lily Yen_, Apr 23 2013