OFFSET
1,2
COMMENTS
Numbers h such that Fibonacci(h) mod 3 = 1. - Bruno Berselli, Oct 18 2017
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
FORMULA
From Chai Wah Wu, May 30 2016: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4), for n > 4.
G.f.: x*(x^3 + 5*x^2 + x + 1)/(x^4 - x^3 - x + 1). (End)
From Wesley Ivan Hurt, Jun 10 2016: (Start)
a(n) = 8*n/3 - 2 + cos(2*n*Pi/3) + 5*sin(2*n*Pi/3)/(3*sqrt(3)).
a(3*k) = 8*k-1, a(3*k-1) = 8*k-6, a(3*k-2) = 8*k-7. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = ((2*sqrt(2+sqrt(2))-1)*Pi + log(3 - 2*sqrt(2)))/(8*sqrt(2)). - Amiram Eldar, Dec 19 2021
MAPLE
A047526:=n->8*n/3-2+cos(2*n*Pi/3)+5*sin(2*n*Pi/3)/(3*sqrt(3)): seq(A047526(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016
MATHEMATICA
LinearRecurrence[{1, 0, 1, -1}, {1, 2, 7, 9}, 50] (* G. C. Greubel, May 30 2016 *)
#+{1, 2, 7}&/@(8*Range[0, 20])//Flatten (* Harvey P. Dale, Oct 17 2021 *)
PROG
(Magma) [n: n in [0..150] | n mod 8 in [1, 2, 7]]; // Wesley Ivan Hurt, Jun 10 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved