OFFSET
1,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
FORMULA
Equals partial sums of (0, 1, 3, 2, 1, 3, 2, 1, 3, 2, ...). - Gary W. Adamson, Jun 19 2008
G.f.: x^2*(1+x)*(2*x+1)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011
From Wesley Ivan Hurt, Jun 14 2016: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
a(n) = (6*n-7+cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/3.
a(3k) = 6k-2, a(3k-1) = 6k-5, a(3k-2) = 6k-6. (End)
Sum_{n>=2} (-1)^n/a(n) = (3-sqrt(3))*Pi/18 + log(2)/3 + log(2+sqrt(3))/(2*sqrt(3)). - Amiram Eldar, Dec 14 2021
E.g.f.: (6 + exp(x)*(6*x - 7) + exp(-x/2)*(cos(sqrt(3)*x/2) + sqrt(3)*sin(sqrt(3)*x/2)))/3. - Stefano Spezia, Jul 26 2024
MAPLE
A047234:=n->(6*n-7+cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/3: seq(A047234(n), n=1..100); # Wesley Ivan Hurt, Jun 14 2016
MATHEMATICA
Select[Range[0, 200], Mod[#, 6] == 0 || Mod[#, 6] == 1 || Mod[#, 6] == 4 &] (* Vladimir Joseph Stephan Orlovsky, Jul 07 2011 *)
LinearRecurrence[{1, 0, 1, -1}, {0, 1, 4, 6}, 100] (* Vincenzo Librandi, Jun 15 2016 *)
#+{0, 1, 4}&/@(6*Range[0, 20])//Flatten (* Harvey P. Dale, Jul 25 2019 *)
PROG
(PARI) a(n)=(n-1)\3*6+[4, 0, 1][n%3+1] \\ Charles R Greathouse IV, Jun 11 2015
(Magma) [n : n in [0..150] | n mod 6 in [0, 1, 4]]; // Wesley Ivan Hurt, Jun 14 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved