OFFSET
1,2
LINKS
Bruce Nye, Table of n, a(n) for n = 1..8500 (terms 1..1000 from Vincenzo Librandi)
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
FORMULA
From R. J. Mathar, Aug 05 2010: (Start)
G.f.: x^2*(3+x+2*x^2) / ( (1+x+x^2)*(x-1)^2 ).
a(n) = a(n-1) + a(n-3) - a(n-4), n>4.
a(n) = 2*n + 2 - (11 + A061347(n+1))/3. (End)
From Wesley Ivan Hurt, Jun 13 2016: (Start)
a(n) = (6*n - 5 - cos(2*n*Pi/3) - sqrt(3)*sin(2*n*Pi/3))/3.
a(3*k) = 6*k-2, a(3*k-1) = 6*k-3, a(3*k-2) = 6*k-6. (End)
Sum_{n>=2} (-1)^n/a(n) = log(2)/3 + (1-2/sqrt(3))*Pi/12. - Amiram Eldar, Dec 14 2021
MAPLE
A047231:=n->(6*n-5-cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/3: seq(A047231(n), n=1..124); # Wesley Ivan Hurt, Jun 13 2016
MATHEMATICA
Select[Range[0, 124], MemberQ[{0, 3, 4}, Mod[#, 6]]&] (* Vincenzo Librandi, Jan 06 2013 *)
(* Alternative: *)
LinearRecurrence[{1, 0, 1, -1}, {0, 3, 4, 6}, 63] (* Harvey P. Dale, Sep 03 2017 *)
PROG
(Magma) [n: n in [0..124] | n mod 6 in [0, 3, 4]]; // Vincenzo Librandi, Jan 06 2013
(PARI) my(s=0); print1(s", "); for(n=1, 62, print1(s+=1+(n-2)%3", ")) \\ Bruce Nye, May 22 2026
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved