A061800 a(n) = n + (-1)^(n mod 3).

1, 0, 3, 4, 3, 6, 7, 6, 9, 10, 9, 12, 13, 12, 15, 16, 15, 18, 19, 18, 21, 22, 21, 24, 25, 24, 27, 28, 27, 30, 31, 30, 33, 34, 33, 36, 37, 36, 39, 40, 39, 42, 43, 42, 45, 46, 45, 48, 49, 48, 51, 52, 51, 54, 55, 54, 57, 58, 57, 60, 61, 60, 63, 64, 63, 66, 67, 66, 69, 70, 69, 72

Offset

0,3

Comments

The arithmetic function v_3(n,3) as defined in A289187. - Robert Price, Aug 22 2017

Links

Harry J. Smith, Table of n, a(n) for n=0..1000

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

Formula

O.g.f.: (1-x+3*x^2)/((-1+x)^2*(1+x+x^2)). - R. J. Mathar, Apr 02 2008

a(n) = (3*n + 1 - 4*cos(2*(n+2)*Pi/3))/3. - Wesley Ivan Hurt, Sep 26 2017

a(n) = a(n-1) + a(n-3) - a(n-4) for n > 3. - Wesley Ivan Hurt, Oct 07 2017

Example

a(4) = 4 + (-1)^1 = 3.

Maple

A061800:=n->n+(-1)^(n mod 3): seq(A061800(n), n=0..150); # Wesley Ivan Hurt, Oct 07 2017

Mathematica

Table[n + (-1)^Mod[n, 3], {n, 0, 80}] (* Vincenzo Librandi, Aug 23 2017 *)

Prog

(PARI) { for (n=0, 1000, write("b061800.txt", n, " ", n + (-1)^(n%3)) ) } \\ Harry J. Smith, Jul 28 2009
(Magma) [n+(-1)^(n mod 3): n in [0..80]]; // Vincenzo Librandi, Aug 23 2017

Crossrefs

Cf. A004442, A014681, A289187.

Sequence in context: A331372 A049276 A101684 * A218789 A324335 A238162

Adjacent sequences: A061797 A061798 A061799 * A061801 A061802 A061803

Keyword

easy,nonn

Author

Olivier Gérard, Jun 22 2001

Status

approved