OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (10,-17,8).
FORMULA
From Vincenzo Librandi, Jun 17 2013: (Start)
G.f.: (1-3*x+9*x^2)/((1-8*x)*(1-x)^2).
a(n) = 10*a(n-1) - 17*a(n-2) + 8*a(n-3). (End)
E.g.f.: exp(x)*(exp(7*x) - x). - Elmo R. Oliveira, Sep 10 2024
MATHEMATICA
Table[8^n - n, {n, 0, 20}] (* or *) CoefficientList[Series[(1 - 3 x + 9 x^2) / ((1 - 8 x) (1 - x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 17 2013 *)
LinearRecurrence[{10, -17, 8}, {1, 7, 62}, 30] (* Harvey P. Dale, Sep 28 2017 *)
PROG
(Magma) [8^n-n: n in [0..20]]; // Vincenzo Librandi, Jul 05 2011
(Magma) I:=[1, 7, 62]; [n le 3 select I[n] else 10*Self(n-1)-17*Self(n-2)+8*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 17 2013
(PARI) a(n)=8^n-n \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved