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+x+x^2+3*x^3+x^4+x^5) / ( (1+x)*(x^2-x+1)*(1+x+x^2)*(x-1)^2 ). - R. J. Mathar, Nov 06 2015
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)+12*cos(n*Pi/3)-4*sqrt(3)*sin(2*n*Pi/3))/18.
a(6k) = 8k-1, a(6k-1) = 8k-2, a(6k-2) = 8k-5, a(6k-3) = 8k-6, a(6k-4) = 8k-7, a(6k-5) = 8k-8. (End)
Sum_{n>=2} (-1)^n/a(n) = (sqrt(2)-1)*Pi/16 + (12-sqrt(2))*log(2)/16 + sqrt(2)*log(sqrt(2)+2)/8. - Amiram Eldar, Dec 26 2021
MAPLE
A047505:=n->(24*n-27-3*cos(n*Pi)+12*cos(n*Pi/3)-4*sqrt(3)*sin(2*n*Pi/3))/18: seq(A047505(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016
MATHEMATICA
Select[Range[0, 100], MemberQ[{0, 1, 2, 3, 6, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 16 2016 *)
PROG
(Magma) [n : n in [0..100] | n mod 8 in [0, 1, 2, 3, 6, 7]]; // Wesley Ivan Hurt, Jun 16 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved