OFFSET
1,2
COMMENTS
Numbers m such that Lucas(m) mod 3 = 1. - Bruno Berselli, Oct 19 2017
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
FORMULA
G.f.: x*(1+2*x+x^2+4*x^3)/((1-x)^2*(1+x+x^2)). - Colin Barker, May 13 2012
From Wesley Ivan Hurt, Jun 09 2016: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
a(n) = 2*(12*n-12-6*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9.
a(3*k) = 8*k-4, a(3*k-1) = 8*k-5, a(3*k-2) = 8*k-7. (End)
MAPLE
A047459:=n->2*(12*n-12-6*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9: seq(A047459(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016
MATHEMATICA
Select[Range[200], MemberQ[{1, 3, 4}, Mod[#, 8]] &] (* or *) LinearRecurrence[{1, 0, 1, -1}, {1, 3, 4, 9}, 60] (* Harvey P. Dale, Nov 26 2015 *)
PROG
(Magma) [n: n in [0..150] | n mod 8 in [1, 3, 4]]; // Wesley Ivan Hurt, Jun 09 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved