A131380 a(3n) = 2n, a(3n+1) = 2n+2, a(3n+2) = 2n+1.

0, 2, 1, 2, 4, 3, 4, 6, 5, 6, 8, 7, 8, 10, 9, 10, 12, 11, 12, 14, 13, 14, 16, 15, 16, 18, 17, 18, 20, 19, 20, 22, 21, 22, 24, 23, 24, 26, 25, 26, 28, 27, 28, 30, 29, 30, 32, 31, 32, 34, 33, 34, 36, 35, 36, 38, 37, 38, 40, 39, 40, 42, 41, 42, 44, 43, 44, 46, 45, 46, 48, 47, 48, 50

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

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

Formula

G.f.: x*(2-x+x^2)/((x-1)^2*(1+x+x^2)); a(n) = a(n-1)+a(n-3)-a(n-4); a(n) = (-n mod 3) + 2*floor(n/3) = A080425(n) + 2*A002264(n). - Wesley Ivan Hurt, Aug 20 2014

E.g.f.: ((2*z+1)/3*exp(z)+((5/9)*sqrt(3)*sin(sqrt(3)*z/2)-(1/3)*cos((sqrt(3)*z/2))*exp(-z/2). - Robert Israel, Aug 21 2014

a(n) = (6*n+3-6*cos(2*(n+4)*Pi/3)-4*sqrt(3)*sin(2*(n+4)*Pi/3))/9. - Wesley Ivan Hurt, Sep 26 2017

Maple

A131380:=n->(-n mod 3) + 2*floor(n/3): seq(A131380(n), n=0..100); # Wesley Ivan Hurt, Aug 20 2014

Mathematica

Table[Mod[-n, 3] + 2 Floor[n/3], {n, 0, 100}] (* Wesley Ivan Hurt, Aug 20 2014 *)
CoefficientList[Series[x*(2 - x + x^2)/((x - 1)^2 (1 + x + x^2)), {x, 0, 100}], x] (* Wesley Ivan Hurt, Aug 20 2014 *)
LinearRecurrence[{1, 0, 1, -1}, {0, 2, 1, 2}, 200] (* Vincenzo Librandi, Sep 27 2017 *)

Prog

(Magma) [(-n mod 3) + 2*Floor(n/3) : n in [0..100]]; // Wesley Ivan Hurt, Aug 20 2014
(Magma) I:=[0, 2, 1, 2]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..100]]; // Vincenzo Librandi, Sep 27 2017

Crossrefs

Cf. A002264, A080425.

Sequence in context: A165053 A302982 A238577 * A100461 A302655 A316997

Adjacent sequences: A131377 A131378 A131379 * A131381 A131382 A131383

Keyword

nonn,easy

Author

Paul Curtz, Oct 01 2007

Status

approved