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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

G. C. Greubel, Table of n, a(n) for n = 0..1000

Harry Crane, Left-right arrangements, set partitions, and pattern avoidance, Australasian Journal of Combinatorics, 61(1) (2015), 57-72.

Index entries for linear recurrences with constant coefficients, signature (9,-29,39,-18).

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

Adjacent sequences:  A163938 A163939 A163940 * A163942 A163943 A163944

KEYWORD

easy,nonn

AUTHOR

Johannes W. Meijer, Aug 13 2009

STATUS

approved

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Last modified December 3 05:05 EST 2021. Contains 349445 sequences. (Running on oeis4.)