A133310 a(3n) = 2n+1, a(3n+1) = 2n+2, a(3n+2) = 2n+1.

1, 2, 1, 3, 4, 3, 5, 6, 5, 7, 8, 7, 9, 10, 9, 11, 12, 11, 13, 14, 13, 15, 16, 15, 17, 18, 17, 19, 20, 19, 21, 22, 21, 23, 24, 23, 25, 26, 25, 27, 28, 27, 29, 30, 29, 31, 32, 31, 33, 34, 33, 35, 36, 35, 37, 38, 37, 39, 40, 39, 41, 42, 41, 43, 44, 43, 45, 46, 45, 47, 48, 47, 49, 50

Offset: 0

Author

Paul Curtz, Oct 18 2007

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Crossrefs

Cf. A130823 (1, 1, 1, 3, 3, 3).

Programs

Magma

Q:=Rationals(); R:=PowerSeriesRing(Q, 70); Coefficients(R!((1+x-x^2+x^3)/((1+x+x^2)*(x-1)^2))) // G. C. Greubel, Feb 10 2018

Mathematica

CoefficientList[Series[(1+x-x^2+x^3)/((1+x+x^2)*(x-1)^2), {x, 0, 50}], x] (* G. C. Greubel, Feb 10 2018 *)
LinearRecurrence[{1, 0, 1, -1}, {1, 2, 1, 3}, 74] (* Robert G. Wilson v, Feb 10 2018 *)

PARI

my(x='x+O('x^70)); Vec((1+x-x^2+x^3)/((1+x+x^2)*(x-1)^2)) \\ G. C. Greubel, Feb 10 2018

Formula

G.f.: ( 1+x-x^2+x^3 ) / ( (1+x+x^2)*(x-1)^2 ). - R. J. Mathar, May 23 2014

a(n) = (2/9)*(3*n+3+3*cos(2*(n-1)*Pi/3)-2*sqrt(3)*sin(2*(n-1)*Pi/3)). - Wesley Ivan Hurt, Sep 30 2017