OFFSET
1,2
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
From R. J. Mathar, Oct 18 2008: (Start)
G.f.: x^2*(3+2*x+3*x^2)/((1-x)^2*(1+x+x^2)).
a(n) = A008576(n-1), for n>1. (End)
a(n) = floor((8n-7)/3). - Gary Detlefs, Mar 07 2010
From Wesley Ivan Hurt, Jun 13 2016: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
a(n) = (24*n-24-3*cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/9.
a(3k) = 8k-3, a(3k-1) = 8k-5, a(3k-2) = 8k-8. (End)
a(n) = A047408(n) - 1. - Lorenzo Sauras Altuzarra, Jan 31 2023
E.g.f.: 3 + (8/3)*exp(x)*(x - 1) - exp(-x/2)*(3*cos(sqrt(3)*x/2) + sqrt(3)*sin(sqrt(3)*x/2))/9. - Stefano Spezia, Mar 30 2023
MAPLE
seq(floor((8*n-7)/3), n=1..52); # Gary Detlefs, Mar 07 2010
MATHEMATICA
Select[Range[0, 150], MemberQ[{0, 3, 5}, Mod[#, 8]]&] (* Harvey P. Dale, Oct 04 2012 *)
LinearRecurrence[{1, 0, 1, -1}, {0, 3, 5, 8}, 100] (* Vincenzo Librandi, Jun 14 2016 *)
PROG
(Magma) [n : n in [0..150] | n mod 8 in [0, 3, 5]]; // Wesley Ivan Hurt, Jun 13 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved