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A131380
a(3n) = 2n, a(3n+1) = 2n+2, a(3n+2) = 2n+1.
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
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
Sequence in context: A165053 A302982 A238577 * A100461 A302655 A316997
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Oct 01 2007
STATUS
approved