OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
FORMULA
G.f.: x*(1+x+4*x^2+x^3) / ( (1+x+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011
From Wesley Ivan Hurt, Jun 07 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (21*n-15+6*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9.
a(3k) = 7k-1, a(3k-1) = 7k-5, a(3k-2) = 7k-6. (End)
MAPLE
A047278:=n->(21*n-15+6*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047278(n), n=1..100); # Wesley Ivan Hurt, Jun 07 2016
MATHEMATICA
Table[(21*n-15+6*Cos[2*n*Pi/3]+4*Sqrt[3]*Sin[2*n*Pi/3])/9, {n,
80}] (* Wesley Ivan Hurt, Jun 07 2016 *)
Select[Range[200], MemberQ[{1, 2, 6}, Mod[#, 7]]&] (* or *) LinearRecurrence[ {1, 0, 1, -1}, {1, 2, 6, 8}, 100] (* Harvey P. Dale, Dec 16 2018 *)
PROG
(Magma) [n : n in [1..150] | n mod 7 in [1, 2, 6]]; // Wesley Ivan Hurt, Jun 07 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved