A225032 Non-crossing, non-nesting, 6-colored set partitions.
1, 7, 55, 493, 5029, 57379, 716443, 9604345, 136236937, 2022864031, 31180099711, 495615409957, 8079827006125, 134488017925243, 2276945808434659, 39088515241450609, 678651272689389073, 11890942901283331255, 209891714523969067207, 3727004974842239659741
Offset: 0
Examples
For n=2, a(2)=55 is the number of non-crossing, non-nesting set partitions on 3 elements with 6 possible arc colors.
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 (63,-1589,20515,-142915,509549,-727767,1).
Programs
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PARI
Vec((1 - 56*x + 1203*x^2 - 12364*x^3 + 60675*x^4 - 113540*x^5 + x^6) / (1 - 63*x + 1589*x^2 - 20515*x^3 + 142915*x^4 - 509549*x^5 + 727767*x^6 - x^7) + O(x^40)) \\ Colin Barker, Jun 22 2019
Formula
G.f.: (1-56*x+1203*x^2-12364*x^3+60675*x^4-113540*x^5+x^6)/ (1-63*x+1589*x^2-20515*x^3+142915*x^4-509549*x^5+727767*x^6-x^7).
a(n) = 63*a(n-1) - 1589*a(n-2) + 20515*a(n-3) - 142915*a(n-4) + 509549*a(n-5) - 727767*a(n-6) + a(n-7) for n>6. - Colin Barker, Jun 22 2019