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,-101,168).
FORMULA
a(n) = (4*8^(n+2) - 5*7^(n+2) + 3^(n+2))/20. [Yahia Kahloune, Jun 30 2013]
a(0)=1, a(1)=18, a(2)=223; for n>2, a(n) = 18*a(n-1) -101*a(n-2) +168*a(n-3). - Vincenzo Librandi, Jul 02 2013
a(n) = 15*a(n-1) -56*a(n-2) +3^n. - Vincenzo Librandi, Jul 02 2013
MATHEMATICA
CoefficientList[Series[1 / ((1 - 3 x) (1 - 7 x) (1 - 8 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 02 2013 *)
LinearRecurrence[{18, -101, 168}, {1, 18, 223}, 20] (* Harvey P. Dale, Jan 01 2022 *)
PROG
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-7*x)*(1-8*x)))); /* or */ I:=[1, 18, 223]; [n le 3 select I[n] else 18*Self(n-1)-101*Self(n-2)+168*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved