A300069 Period 6: repeat [0, 0, 0, 1, 2, 1].

0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 2, 1

Offset: 0

Author

Wolfdieter Lang, Feb 24 2018

Keywords

• nonn
• easy

Comments

Underlying A174257(n+1), n >= 0.

Links

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

Crossrefs

Cf. A174257, A300067.

Programs

Mathematica

PadRight[{}, 102, {0, 0, 0, 1, 2, 1}] (* or *)
CoefficientList[Series[x^3*(1 + x)^2/(1 - x^6), {x, 0, 102}], x] (* Michael De Vlieger, Feb 25 2018 *)

PARI

a(n) = my(v=[0, 0, 1, 2, 1]); v[if(n%6==0, 1, n%6)] \\ Felix Fröhlich, Feb 24 2018

PARI

concat(vector(3), Vec(x^3*(1 + x)^2/(1 - x^6) + O(x^40))) \\ Felix Fröhlich, Feb 25 2018

Formula

a(n) = floor((n (mod 6))/3) + floor((n + 1 (mod 6))/5), n >= 0.

G.f.: x^3*(1 + x)^2/(1 - x^6) = -x^3*(1+x)/(x-1)/(1+x+x^2)/(1-x+x^2).

a(n) = (4 - 3*cos(n*Pi/3) - cos(2*n*Pi/3) - 3*sqrt(3)*sin(n*Pi/3) + sqrt(3)*sin(2*n*Pi/3))/6. - Wesley Ivan Hurt, Oct 04 2018