A225030 Non-crossing, non-nesting, 4-colored set partitions.
1, 5, 29, 193, 1441, 11765, 102701, 941857, 8955937, 87439877, 870218525, 8780788513, 89476873345, 918150779957, 9467752541933, 97965021468865, 1016097175530433, 10556565963815045, 109802406545873309, 1143006276663287809, 11904902286515536609
Offset: 0
Examples
For n=3, a(3)=193 is the number of non-crossing, non-nesting, 4-colored set partitions on 4 elements.
Links
- Lily Yen, Table of n, a(n) for n = 0..99
- Eric Marberg, Crossings and nestings in colored set partitions, arXiv preprint arXiv:1203.5738 [math.CO], 2012-2013.
- Lily Yen, Crossings and Nestings for Arc-Coloured Permutations, arXiv:1211.3472 [math.CO], 2012-2013 and Arc-coloured permutations, PSAC 2013, Paris, France, June 24-28, Proc. DMTCS (2013) 743-754
- Lily Yen, Crossings and Nestings for Arc-Coloured Permutations and Automation, Electronic Journal of Combinatorics, 22(1) (2015), #P1.14.
- Index entries for linear recurrences with constant coefficients, signature (25,-218,782,-973,1).
Programs
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Mathematica
LinearRecurrence[{25, -218, 782, -973, 1}, {1, 5, 29, 193, 1441}, 25] (* Paolo Xausa, Feb 06 2024 *)
Formula
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).