OFFSET
1,3
LINKS
Vincenzo Librandi, 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, Jun 10 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).
G.f.: x^2*(x^4 + x^2 + x + 1)/((x - 1)^2*(x^2 - x + 1)*(x^2 + x + 1 ) ). (End)
a(n) = (12*n - 3*sqrt(3)*sin(Pi*n/3) + sqrt(3)*sin(2*Pi*n/3) - 9)/9. - Ilya Gutkovskiy, Jun 11 2016
a(3k) = 8k-1, a(3k-1) = 8k-2, a(3k-2) = 8k-3, a(3k-3) = 8k-5, a(3k-4) = 8k-7, a(3k-5) = 8k-8. - Wesley Ivan Hurt, Jun 16 2016
Sum_{n>=2} (-1)^n/a(n) = (3-2*sqrt(2))*Pi/16 + (5-sqrt(2))*log(2)/8 + sqrt(2)*log(sqrt(2)+2)/4. - Amiram Eldar, Dec 27 2021
MAPLE
A047585:=n->(12*n - 3*sqrt(3)*sin(Pi*n/3) + sqrt(3)*sin(2*Pi*n/3) - 9)/9: seq(A047585(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016
MATHEMATICA
Select[Range[0, 100], MemberQ[{0, 1, 3, 5, 6, 7}, Mod[#, 8]]&] (* or *) Complement[Range[0, 100], Flatten[Range[{2, 4}, 100, 8]]] (* Harvey P. Dale, May 01 2012 *)
CoefficientList[Series[x (x^4 + x^2 + x + 1) / ((x - 1)^2 (x^2 - x + 1) (x^2 + x + 1)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 18 2016 *)
PROG
(Magma) [n : n in [0..100] | n mod 8 in [0, 1, 3, 5, 6, 7]]; // Wesley Ivan Hurt, Jun 16 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 11 1999
STATUS
approved