OFFSET
1,1
LINKS
Stefano Spezia, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
FORMULA
G.f.: x*(2+x+x^2+x^3) / ((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 07 2011
From Wesley Ivan Hurt, Jun 14 2016: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n>3.
a(n) = (15*n-3-6*cos(2*n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/9.
a(3k) = 5k-1, a(3k-1) = 5k-2, a(3k-2) = 5k-3. (End)
a(n) = 2*n - floor((n-1)/3) - ((n-1) mod 3). - Wesley Ivan Hurt, Sep 26 2017
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt((5+sqrt(5))/10)*Pi/5 + log(phi)/sqrt(5) - 3*log(2)/5, where phi is the golden ratio (A001622). - Amiram Eldar, Apr 16 2023
MAPLE
A047202:=n->(15*n-3-6*cos(2*n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047202(n), n=1..100); # Wesley Ivan Hurt, Jun 14 2016
MATHEMATICA
Select[Range[0, 200], MemberQ[{2, 3, 4}, Mod[#, 5]] &] (* Vladimir Joseph Stephan Orlovsky, Feb 12 2012 *)
PROG
(Magma) [n: n in [1..150] | n mod 5 in [2..4]]; // Vincenzo Librandi, Mar 31 2011
(PARI) a(n)=n\3*5+[-1, 2, 3][n%3+1] \\ Charles R Greathouse IV, Dec 22 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved