OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (20,-111,180).
FORMULA
a(0)=1, a(1)=20, a(2)=289; for n>2, a(n) = 20*a(n-1) -111*a(n-2) +180*a(n-3). - Vincenzo Librandi, Jul 02 2013
a(n) = 17*a(n-1) -60*a(n-2) +3^n. - Vincenzo Librandi, Jul 02 2013
a(n) = (2*12^(n+2) - 9*5^(n+2) + 7*3^(n+2))/126. [Yahia Kahloune, Jul 06 2013]
MAPLE
a:= n-> (Matrix(3, (i, j)-> `if`(i=j-1, 1, `if`(j=1, [20, -111, 180][i], 0)))^n)[1, 1]: seq(a(n), n=0..25); # Alois P. Heinz, Jul 02 2013
MATHEMATICA
CoefficientList[Series[1 / ((1 - 3 x) (1 - 5 x) (1 - 12 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 02 2013 *)
LinearRecurrence[{20, -111, 180}, {1, 20, 289}, 20] (* Harvey P. Dale, Aug 22 2019 *)
PROG
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-5*x)*(1-12*x)))); /* or */ I:=[1, 20, 289]; [n le 3 select I[n] else 20*Self(n-1)-111*Self(n-2)+180*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved