OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (25,-204,540).
FORMULA
a(0)=1, a(1)=25, a(2)=421; For n>2, a(n) = 25*a(n-1)-204*a(n-2)+540*a(n-3). - Harvey P. Dale, Oct 13 2012
a(n) = (3*10^(n+2) - 4*9^(n+2) + 6^(n+2))/12. [Yahia Kahloune, Jun 30 2013]
a(n) = 19*a(n-1) -90*a(n-2) +6^n. - Vincenzo Librandi, Jul 04 2013
MATHEMATICA
CoefficientList[Series[1 / ((1 - 6 x) (1 - 9 x) (1 - 10 x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{25, -204, 540}, {1, 25, 421}, 20] (* Harvey P. Dale, Oct 13 2012 *)
PROG
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-6*x)*(1-9*x)*(1-10*x)))); /* or */ I:=[1, 25, 421]; [n le 3 select I[n] else 25*Self(n-1)-204*Self(n-2)+540*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 04 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved