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,-99,202,-120).
FORMULA
a(0)=1, a(1)=18, a(2)=225, a(3)=2470, a(n)=18*a(n-1)- 99*a(n-2)+ 202*a(n-3)- 120*a(n-4). - Harvey P. Dale, Oct 21 2011
a(0)=1, a(1)=18; for n>1, a(n) = 14*a(n-1) -40*a(n-2) +(3^n-1)/2. - Vincenzo Librandi, Jul 09 2013
a(n) = (10^(n+3) - 21*4^(n+3) + 27*3^(n+3) - 7)/378. - Yahia Kahloune, Sep 16 2013
MATHEMATICA
CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 4 x) (1 - 10 x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{18, -99, 202, -120}, {1, 18, 225, 2470}, 30] (* Harvey P. Dale, Oct 21 2011 *)
PROG
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-4*x)*(1-10*x)))); // Vincenzo Librandi, Jul 09 2013
(Magma) I:=[1, 18, 225, 2470]; [n le 4 select I[n] else 18*Self(n-1)-99*Self(n-2)+202*Self(n-3)-120*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 09 2013
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
STATUS
approved