OFFSET
1,2
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
From R. J. Mathar, Dec 05 2011: (Start)
a(n) = 2*A004772(n).
G.f.: 2*x^2*(2+x+x^2) / ((1+x+x^2)*(x-1)^2). (End)
From Wesley Ivan Hurt, Jun 10 2016: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
a(n) = 2*(12*n-9-2*sqrt(3)*sin(2*n*Pi/3))/9.
a(3k) = 8k-2, a(3k-1) = 8k-4, a(3k-2) = 8k-8. (End)
a(n) = 2*(n - 1 + floor((n + 1)/3)). - Wolfdieter Lang, Sep 11 2021
Sum_{n>=2} (-1)^n/a(n) = (2-sqrt(2))*log(2)/16 + sqrt(2)*log(sqrt(2)+2)/8 - (sqrt(2)-1)*Pi/16. - Amiram Eldar, Dec 19 2021
MAPLE
A047407:=n->2*(12*n-9-2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047407(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016
MATHEMATICA
Select[Range[0, 200], MemberQ[{0, 4, 6}, Mod[#, 8]]&] (* or *) LinearRecurrence[{1, 0, 1, -1}, {0, 4, 6, 8}, 70] (* Harvey P. Dale, Apr 20 2016 *)
PROG
(Magma) [n : n in [0..160] | n mod 8 in [0, 4, 6]]; // Vincenzo Librandi, May 02 2016
(PARI) a(n)=n\3*8+[-2, 0, 4][n%3+1] \\ Charles R Greathouse IV, May 02 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved