OFFSET
0,2
COMMENTS
LINKS
FORMULA
a(n) = a(n-3) for n > 2, with a(0) = 1, a(1) = 3, a(2) = 3.
G.f.: (1+3*x+3*x^2)/(1-x^3).
a(n) = (7/3)+(2/3)*cos((2*Pi/3)*(n+1))-(2*sqrt(3)/3)*sin((2*Pi/3)*(n+1)). [Richard Choulet, Mar 15 2010]
a(n) = a(n-a(n-2)) for n>=2. Example: a(5) = a(5-a(3)) = a(5-a(3-a(1))) = a(5-a(3-3)) = a(5-a(0)) = a(5-1) = a(4) = a(4-a(2)) = a(4-3) = a(1) = 3. [Richard Choulet, Mar 15 2010; edited by Klaus Brockhaus, Nov 21 2010]
a(n) = 1 + 2*sgn(n mod 3). - Wesley Ivan Hurt, Jul 02 2016
a(n) = 3/gcd(n,3). - Wesley Ivan Hurt, Jul 11 2016
MAPLE
seq(op([1, 3, 3]), n=0..50); # Wesley Ivan Hurt, Jul 02 2016
MATHEMATICA
PadRight[{}, 120, {1, 3, 3}] (* or *) LinearRecurrence[{0, 0, 1}, {1, 3, 3}, 120] (* Harvey P. Dale, Apr 29 2015 *)
PROG
(Magma) [ n mod 3 eq 0 select 1 else 3: n in [0..104] ];
(Magma) &cat [[1, 3, 3]^^30]; // Wesley Ivan Hurt, Jul 02 2016
CROSSREFS
KEYWORD
AUTHOR
Klaus Brockhaus, Dec 03 2009
EXTENSIONS
Keywords cofr, cons added by Klaus Brockhaus, Apr 20 2010
Minor edits, crossref added by Klaus Brockhaus, May 03 2010
STATUS
approved