A080425 Period 3: repeat [0, 2, 1].

0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1

Offset: 0

Author

Paul Barry, Feb 20 2003

Keywords

• nonn
• easy

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

• Index entries for linear recurrences with constant coefficients, signature (0,0,1).

Crossrefs

Cf. A001045, A001477, A007318, A010872, A130196, A131534.

Programs

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

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 *)

PARI

a(n)=2*n%3 \\ Charles R Greathouse IV, Sep 24 2015

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) = A130196(n) + A131534(n) - 2. - Reinhard Zumkeller, Nov 12 2009

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)

Extensions

More terms from Reinhard Zumkeller, Jul 30 2005

New name from Joerg Arndt, Apr 21 2014