OFFSET
1,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
FORMULA
G.f.: x*(3+2*x+2*x^2+x^3)/((1-x)^2*(1+x+x^2)). [Colin Barker, May 14 2012]
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4. - Vincenzo Librandi, May 17 2012
From Wesley Ivan Hurt, Jun 10 2016: (Start)
a(n) = (24*n-3-6*cos(2*n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/9.
a(3k) = 8k-1, a(3k-1) = 8k-3, a(3k-2) = 8k-5. (End)
a(n) = 3*n - floor((n-1)/3) - ((n-1) mod 3). - Wesley Ivan Hurt, Sep 26 2017
a(n) = 2*(n + floor((n-1)/3)) + 1. - Wolfdieter Lang, Sep 11 2021
MAPLE
A047484:=n->(24*n-3-6*cos(2*n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047484(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016
MATHEMATICA
Select[Range[0, 300], MemberQ[{3, 5, 7}, Mod[#, 8]]&] (* Vincenzo Librandi, May 17 2012 *)
PROG
(Magma) I:=[3, 5, 7, 11]; [n le 4 select I[n] else Self(n-1)+Self(n-3) -Self(n-4): n in [1..70]]; // Vincenzo Librandi, May 17 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved