OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (19,-111,189).
FORMULA
a(0)=1, a(1)=19, a(2)=250, a(n)=19*a(n-1)-111*a(n-2)+189*a(n-3). - Harvey P. Dale, Oct 31 2011
a(n) = (2*9^(n+2) - 3*7^(n+2) + 3^(n+2))/24. - Yahia Kahloune, Jun 30 2013
a(n) = 16*a(n-1) -63*a(n-2) +3^n. - Vincenzo Librandi, Jul 02 2013
MAPLE
a:= n-> (Matrix(3, (i, j)-> `if`(i=j-1, 1, `if`(j=1, [19, -111, 189][i], 0)))^n)[1, 1]: seq(a(n), n=0..25); # Alois P. Heinz, Jul 02 2013
MATHEMATICA
CoefficientList[Series[1/((1-3x)(1-7x)(1-9x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{19, -111, 189}, {1, 19, 250}, 30] (* Harvey P. Dale, Oct 31 2011 *)
PROG
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-7*x)*(1-9*x)))); /* or */ I:=[1, 19, 250]; [n le 3 select I[n] else 19*Self(n-1)-111*Self(n-2)+189*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved