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A018911 Expansion of 1/((1-4x)(1-5x)(1-9x)). 1
1, 18, 223, 2376, 23485, 222894, 2067787, 18935172, 172107529, 1557684810, 14063797111, 126801537408, 1142367430933, 10287141958566, 92613721463395, 833671786093884, 7503791834428897, 67537872487648962 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (18,-101,180).

FORMULA

a(n) = 16*4^n/5 -25*5^n/4 +81*9^n/20. - R. J. Mathar, Jun 29 2013

a(0)=1, a(1)=18, a(2)=223; for n>2, a(n)= 18*a(n-1) -101*a(n-2) +180*a(n-3). - Vincenzo Librandi, Jul 02 2013

a(n) = 14*a(n-1) -45*a(n-2) +4^n. - Vincenzo Librandi, Jul 02 2013

MATHEMATICA

CoefficientList[Series[ 1 / ((1 - 4 x) (1 - 5 x) (1 - 9 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 02 2013 *)

LinearRecurrence[{18, -101, 180}, {1, 18, 223}, 30] (* Harvey P. Dale, Jun 22 2017 *)

PROG

(MAGMA) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-5*x)*(1-9*x)))); /* or */ I:=[1, 18, 223]; [n le 3 select I[n] else 18*Self(n-1)-101*Self(n-2)+180*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013

CROSSREFS

Sequence in context: A021454 A021224 A017997 * A021194 A155049 A155073

Adjacent sequences:  A018908 A018909 A018910 * A018912 A018913 A018914

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 28 17:59 EDT 2021. Contains 348329 sequences. (Running on oeis4.)