OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (19,-116,224).
FORMULA
a(n) = (3*8^(n+2)-4*7^(n+2)+4^(n+2))/12. [Yahia Kahloune, May 06 2013]
a(0)=1, a(1)=19, a(2)=245; for n>2, a(n) = 19*a(n-1) -116*a(n-2) +224*a(n-3). - Vincenzo Librandi, Jul 03 2013
a(n) = 15*a(n-1) -56*a(n-2) +4^n. - Vincenzo Librandi, Jul 03 2013
MATHEMATICA
CoefficientList[Series[1 / ((1 - 4 x) (1 - 7 x) (1 - 8 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)
LinearRecurrence[{19, -116, 224}, {1, 19, 245}, 20] (* Harvey P. Dale, Sep 26 2019 *)
PROG
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-7*x)*(1-8*x)))); /* or */ I:=[1, 19, 245]; [n le 3 select I[n] else 19*Self(n-1)-116*Self(n-2)+224*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jl 03 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved