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)))); /* 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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved