OFFSET
1,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,2,-1).
FORMULA
From Chai Wah Wu, May 30 2016: (Start)
a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-2*a(n-4)+2*a(n-5)-a(n-6) for n>6.
G.f.: x^2*(x^4 + x^2 + 2)/((x - 1)^2*(x^2 - x + 1)*(x^2 + x + 1)). (End)
a(n) = (8*n - 2*sqrt(3)*sin(Pi*(n+1)/3) + 2*sin(2*Pi*(n+1)/3)/sqrt(3) - 4)/6. - Ilya Gutkovskiy, May 30 2016
a(6k) = 8k-1, a(6k-1) = 8k-2, a(6k-2) = 8k-3, a(6k-3) = 8k-4, a(6k-4) = 8k-6, a(6k-5) = 8k-8. - Wesley Ivan Hurt, Jun 16 2016
Sum_{n>=2} (-1)^n/a(n) = 3*log(2)/4 - (sqrt(2)-1)*Pi/8. - Amiram Eldar, Dec 27 2021
MAPLE
A047571:=n->(8*n-2*sqrt(3)*sin(Pi*(n+1)/3)+2*sin(2*Pi*(n+1)/3)/sqrt(3)-4)/6: seq(A047571(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016
MATHEMATICA
LinearRecurrence[{2, -2, 2, -2, 2, -1}, {0, 2, 4, 5, 6, 7} , 50] (* G. C. Greubel, May 30 2016 *)
PROG
(Magma) [n: n in [0..200] | n mod 8 in [0, 2, 4, 5, 6, 7]]; // Vincenzo Librandi, May 30 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved