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

0,2

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).

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).

Example

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

Mathematica

LinearRecurrence[{25, -218, 782, -973, 1}, {1, 5, 29, 193, 1441}, 25] (* Paolo Xausa, Feb 06 2024 *)

Crossrefs

Sequence in context: A367240 A171267 A258314 * A188143 A095000 A086672

Adjacent sequences: A225027 A225028 A225029 * A225031 A225032 A225033

Keyword

nonn,easy

Author

Lily Yen, Apr 25 2013

Status

approved