OFFSET
1,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).
FORMULA
G.f.: x^2*(1+2*x+x^2+x^3+x^4+2*x^5) / ((1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2). - R. J. Mathar, Dec 07 2011
From Wesley Ivan Hurt, Jun 16 2016: (Start)
a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.
a(n) = (24*n-27-3*cos(n*Pi)-6*cos(n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/18.
a(6k) = 8k-2, a(6k-1) = 8k-3, a(6k-2) = 8k-4, a(6k-3) = 8k-5, a(6k-4) = 8k-7, a(6k-5) = 8k-8. (End)
Sum_{n>=2} (-1)^n/a(n) = sqrt(2)*Pi/16 + log(2)/8 - sqrt(2)*log(99-70*sqrt(2))/16. - Amiram Eldar, Dec 27 2021
MAPLE
A047428:=n->(24*n-27-3*cos(n*Pi)-6*cos(n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/18: seq(A047428(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016
MATHEMATICA
Select[Range[0, 100], MemberQ[{0, 1, 3, 4, 5, 6}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 16 2016 *)
PROG
(Magma) [n : n in [0..100] | n mod 8 in [0, 1, 3, 4, 5, 6]]; // Wesley Ivan Hurt, Jun 16 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved