OFFSET
0,2
LINKS
Muniru A Asiru, Table of n, a(n) for n = 0..1145 (first 100 terms from Lily Yen)
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(14,-59,74,-1).
FORMULA
G.f.: (1 - 10*x + 22*x^2 - x^3)/(1 - 14*x + 59*x^2 - 74*x^3 + x^4).
a(n) = 14*a(n-1) -59*a(n-2) +74*a(n-3) -a(n-4), with a(0) = 1, a(1) = 4, a(2) = 19 and a(3) = 103. - Muniru A Asiru, Dec 18 2018
EXAMPLE
a(3) = 103 is the number of non-crossing, non-nesting, 3-colored set partitions on {1,2,3,4}.
MAPLE
seq(coeff(series((1-10*x+22*x^2-x^3)/(1-14*x+59*x^2-74*x^3+x^4), x, n+1), x, n), n = 0 .. 25); # Muniru A Asiru, Dec 18 2018
MATHEMATICA
LinearRecurrence[{14, -59, 74, -1}, {1, 4, 19, 103}, 23] (* Jean-François Alcover, Dec 14 2018 *)
CoefficientList[Series[(1 - 10 x + 22 x^2 - x^3) / (1 - 14 x + 59 x^2 - 74 x^3 + x^4), {x, 0, 25}], x] (* Vincenzo Librandi, Dec 20 2018 *)
PROG
(PARI) Vec((1-10*x+22*x^2-x^3)/(1-14*x+59*x^2-74*x^3+x^4)+O(x^66)) \\ Joerg Arndt, Apr 24 2013
(GAP) a:=[1, 4, 19, 103];; for n in [5..25] do a[n]:=14*a[n-1]-59*a[n-2]+74*a[n-3]-a[n-4]; od; a; # Muniru A Asiru, Dec 18 2018
(Magma) I:=[1, 4, 19, 103]; [n le 4 select I[n] else 14*Self(n-1)-59*Self(n-2)+74*Self(n-3)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 20 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Lily Yen, Apr 24 2013
STATUS
approved