OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
FORMULA
G.f.: x*(1+x)*(2*x^2+1)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011
From Wesley Ivan Hurt, Jun 10 2016: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
a(n) = (6*n-5-cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/3.
a(3k) = 6k-2, a(3k-1) = 6k-4, a(3k-2) = 6k-5. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/6 + log(2+sqrt(3))/(2*sqrt(3)) - log(2)/3. - Amiram Eldar, Dec 14 2021
MAPLE
A047236:=n->(6*n-5-cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/3: seq(A047236(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016
MATHEMATICA
Select[Range[0, 150], MemberQ[{1, 2, 4}, Mod[#, 6]] &] (* Wesley Ivan Hurt, Jun 10 2016 *)
PROG
(Magma) [n : n in [0..150] | n mod 6 in [1, 2, 4]]; // Wesley Ivan Hurt, Jun 10 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved