A018911 Expansion of 1/((1-4x)(1-5x)(1-9x)).

1, 18, 223, 2376, 23485, 222894, 2067787, 18935172, 172107529, 1557684810, 14063797111, 126801537408, 1142367430933, 10287141958566, 92613721463395, 833671786093884, 7503791834428897, 67537872487648962

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

From Vincenzo Librandi, Jul 02 2013: (Start)

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

a(n) = 14*a(n-1) - 45*a(n-2) + 4^n. (End)

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)))); // Vincenzo Librandi, Jul 02 2013
(Magma) 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,changed

Author

N. J. A. Sloane

Status

approved