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
Examples
a(4) = 4 + (-1)^1 = 3.
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).
Programs
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Magma
[n+(-1)^(n mod 3): n in [0..80]]; // Vincenzo Librandi, Aug 23 2017
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Maple
A061800:=n->n+(-1)^(n mod 3): seq(A061800(n), n=0..150); # Wesley Ivan Hurt, Oct 07 2017
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Mathematica
Table[n + (-1)^Mod[n, 3], {n, 0, 80}] (* Vincenzo Librandi, Aug 23 2017 *) -
PARI
a(n) = { n + (-1)^(n%3) } \\ Harry J. Smith, Jul 28 2009
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
a(n) = n + 2 - gcd(n+2,3). - Ridouane Oudra, Dec 28 2024
Sum_{n>=2} (-1)^n/a(n) = Pi/(3*sqrt(3)) + log(2) - 1. - Amiram Eldar, Jan 15 2025
Comments