A225030 - OEIS

%I #26 Feb 06 2024 08:13:31

%S 1,5,29,193,1441,11765,102701,941857,8955937,87439877,870218525,

%T 8780788513,89476873345,918150779957,9467752541933,97965021468865,

%U 1016097175530433,10556565963815045,109802406545873309,1143006276663287809,11904902286515536609

%N Non-crossing, non-nesting, 4-colored set partitions.

%H Lily Yen, <a href="/A225030/b225030.txt">Table of n, a(n) for n = 0..99</a>

%H Eric Marberg, <a href="http://arxiv.org/abs/1203.5738">Crossings and nestings in colored set partitions</a>, arXiv preprint arXiv:1203.5738 [math.CO], 2012-2013.

%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 and <a href="https://doi.org/10.46298/dmtcs.2339">Arc-coloured permutations</a>, PSAC 2013, Paris, France, June 24-28, Proc. DMTCS (2013) 743-754

%H Lily Yen, <a href="https://doi.org/10.37236/4080">Crossings and Nestings for Arc-Coloured Permutations and Automation</a>, Electronic Journal of Combinatorics, 22(1) (2015), #P1.14.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (25,-218,782,-973,1).

%F G.f.: (1-20*x+122*x^2-224*x^3+x^4)/(1-25*x +218*x^2-782*x^3+973*x^4-x^5).

%e For n=3, a(3)=193 is the number of non-crossing, non-nesting, 4-colored set partitions on 4 elements.

%t LinearRecurrence[{25, -218, 782, -973, 1}, {1, 5, 29, 193, 1441}, 25] (* _Paolo Xausa_, Feb 06 2024 *)

%K nonn,easy

%O 0,2

%A _Lily Yen_, Apr 25 2013