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A163941 Fourth right hand column of triangle A163940. 4
1, 9, 52, 246, 1039, 4083, 15274, 55152, 193957, 668397, 2266816, 7589418, 25143355, 82571751, 269173078, 871958244, 2809322833, 9008574945, 28768068460, 91532284830, 290283189991, 917912770779, 2894936303362 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Harry Crane, Left-right arrangements, set partitions, and pattern avoidance, Australasian Journal of Combinatorics, 61(1) (2015), 57-72.
FORMULA
G.f.: 1/((1-x)*(1-2*x)*(1-3*x)^2).
a(n) = (1/4)*(2^(n+5) + (2*n - 3)*3^(n+2) - 1).
a(n) = 9*a(n-1) - 29*a(n-2) + 39*a(n-3) - 18*a(n-4).
E.g.f.: (1/4)*(32*exp(2*x) + 27*(2*x-1)*exp(3*x) - exp(x)). - G. C. Greubel, Aug 13 2017
MATHEMATICA
LinearRecurrence[{9, -29, 39, -18}, {1, 9, 52, 246}, 30] (* or *) CoefficientList[ Series[1/((1-x)(1-2x)(1-3x)^2), {x, 0, 30}], x] (* Harvey P. Dale, Aug 14 2011 *)
PROG
(PARI) Vec(1/((1-x)*(1-2*x)*(1-3*x)^2) + O(x^30)) \\ Michel Marcus, Feb 12 2015
CROSSREFS
Equals the fourth right hand column of A163940.
A163942 is another right hand column.
Sequence in context: A197722 A172470 A120665 * A289418 A292488 A282179
KEYWORD
easy,nonn
AUTHOR
Johannes W. Meijer, Aug 13 2009
STATUS
approved

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Last modified July 12 20:37 EDT 2024. Contains 374252 sequences. (Running on oeis4.)