OFFSET
0,2
COMMENTS
Previous name was: Jacobsthal selector sequence.
The Jacobsthal sequence A001045 can be defined by A001045(n) = Sum_{k=0..floor(n,3)} C(n, a(n-1)+3*k).
The floor of the area under the polygon connecting the lattice points: (n, a(n)) from 0..n is A001477(n), the nonnegative integers. - Wesley Ivan Hurt, Jun 16 2014
LINKS
FORMULA
a(n) = ceiling(((n mod 3) + 1)/2) + (-1)^((n mod 3) + 1).
G.f.: x*(x+2)/(1-x^3). - Paul Barry, May 25 2003
a(n) = (3 - (n mod 3)) mod 3. - Reinhard Zumkeller, Jul 30 2005
a(n) = 2 * A001045(L(n/3)), where L(j/p) is the Legendre symbol of j and p.
a(n) = (-n) mod 3; also a(n) = 3*ceiling(n/3)-n. - Hieronymus Fischer, May 29 2007
a(n) = (2n) mod 3. - Wesley Ivan Hurt, Jun 23 2013
From Wesley Ivan Hurt, Jul 02 2016: (Start)
a(n) = a(n-3) for n>2.
a(n) = 2*sin(n*Pi/3)*(3*sin(n*Pi/3) + sqrt(3)*cos(n*Pi/3))/3. (End)
MAPLE
seq(modp(2*n, 3), n=0..90); # Zerinvary Lajos, Dec 01 2006
MATHEMATICA
Table[Mod[-n, 3], {n, 0, 100}] (* Wesley Ivan Hurt, Jun 16 2014 *)
PROG
(Haskell)
a080425 = (`mod` 3) . (3 -) . (`mod` 3)
a080425_list = cycle [0, 2, 1] -- Reinhard Zumkeller, Feb 22 2013
(Magma) [-n mod 3 : n in [0..100]]; // Wesley Ivan Hurt, Jun 16 2014
(PARI) a(n)=2*n%3 \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Feb 20 2003
EXTENSIONS
More terms from Reinhard Zumkeller, Jul 30 2005
New name from Joerg Arndt, Apr 21 2014
STATUS
approved