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,-115,240,-144).
FORMULA
a(0)=1, a(1)=20, a(2)=285, a(3)=3640, a(n) = 20*a(n-1)-115*a(n-2)+240*a(n-3)- 144*a(n-4). [Harvey P. Dale, May 06 2012]
a(0)=1, a(1)=20; for n>1, a(n) = 16*a(n-1) -48*a(n-2) +(3^n-1)/2. - Vincenzo Librandi, Jul 09 2013
MATHEMATICA
CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 4 x) (1 - 12 x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{20, -115, 240, -144}, {1, 20, 285, 3640}, 30] (* Harvey P. Dale, May 06 2012 *)
PROG
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-4*x)*(1-12*x)))); /* or */ I:=[1, 20, 285, 3640]; [n le 4 select I[n] else 20*Self(n-1)-115*Self(n-2)+240*Self(n-3)-144*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 09 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved