OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..100
Index entries for linear recurrences with constant coefficients, signature (17,-80,100).
FORMULA
a(n) = 17*a(n-1) - 80*a(n-2) + 100*a(n-3); a(0)=1, a(1)=17, a(2)=209. - Harvey P. Dale, Aug 24 2011
a(n) = 15*a(n-1) - 50*a(n-2) + 2^n; a(0)=1, a(1)=17. - Vincenzo Librandi, Aug 25 2011
a(n) = (1/6)*(2^n - 10*5^n + 15*10^n). - Bruno Berselli, Aug 25 2011
MATHEMATICA
CoefficientList[Series[1/((1-2x)(1-5x)(1-10x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{17, -80, 100}, {1, 17, 209}, 30] (* Harvey P. Dale, Aug 24 2011 *)
PROG
(Magma) [ n eq 1 select 1 else n eq 2 select 17 else n eq 3 select 209 else 17*Self(n-1)-80*Self(n-2) +100*Self(n-3): n in [1..20] ]; // Vincenzo Librandi, Aug 25 2011
(Magma) /*By definition*/ m:=18; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-2*x)*(1-5*x)*(1-10*x)))); // Bruno Berselli, Aug 25 2011
(PARI) Vec(1/((1-2*x)*(1-5*x)*(1-10*x))+O(x^18)) \\ Bruno Berselli, Aug 25 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved