OFFSET
1,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
a(n) = 8*n - a(n-1) - 4, with n>1, a(1)=6.
From Vincenzo Librandi, Sep 18 2013: (Start)
G.f.: 2*x*(3 + x^2)/((1+x)*(x-1)^2).
a(n) = a(n-1) + a(n-2) - a(n-3).
a(n) = 6 + 8*floor((n-1)/2). (End)
E.g.f.: 2*(-1 + exp(x) + 2*x*exp(2*x))*exp(-x). - G. C. Greubel, Jul 19 2016
MATHEMATICA
CoefficientList[Series[(6 + 2 x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 18 2013 *)
LinearRecurrence[{1, 1, -1}, {6, 6, 14}, 70] (* Harvey P. Dale, Mar 14 2023 *)
PROG
(Magma) [4*n -2*(-1)^n: n in [1..70]]; // Vincenzo Librandi, Sep 18 2013
(Magma) [6+8*Floor((n-1)/2): n in [1..70]]; // Vincenzo Librandi, Sep 18 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Nov 24 2009
EXTENSIONS
Definition rewritten by Vincenzo Librandi, Sep 18 2013
STATUS
approved