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 (1,0,0,0,0,1,-1).
FORMULA
From Chai Wah Wu, May 29 2016: (Start)
a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.
G.f.: x^2*(x^5 + x^4 + x^3 + x^2 + x + 3)/(x^7 - x^6 - x + 1). (End)
From Wesley Ivan Hurt, Jun 16 2016: (Start)
a(n) = (24*n-9+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-3, a(6k-3) = 8k-4, a(6k-4) = 8k-5, a(6k-5) = 8k-8. (End)
Sum_{n>=2} (-1)^n/a(n) = 7*log(2)/8 + sqrt(2)*log(3-2*sqrt(2))/16 - sqrt(2)*Pi/16. - Amiram Eldar, Dec 27 2021
MAPLE
A047563:=n->(24*n-9+3*cos(n*Pi)-12*cos(n*Pi/3)-4*sqrt(3)*sin(2*n*Pi/3))/18: seq(A047563(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016
MATHEMATICA
LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 3, 4, 5, 6, 7, 8}, 50] (* G. C. Greubel, May 29 2016 *)
PROG
(Magma) [n : n in [0..100] | n mod 8 in [0] cat [3..7]]; // Wesley Ivan Hurt, May 29 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved