A300067 Period 6: repeat [0, 0, 0, 1, 2, 2].

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

Offset: 0

Author

Wolfdieter Lang, Feb 24 2018

Keywords

• nonn
• easy

Comments

Used for A300068.

Links

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

Crossrefs

Cf. A300068.

Programs

Mathematica

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

PARI

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

PARI

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

Formula

a(n) = floor((n (mod 6))/3) + floor((n (mod 6))/4), n >= 0.

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

a(n) = (5 - 2*cos(n*Pi/3) - 2*cos(2*n*Pi/3) - cos(n*Pi) - 4*sqrt(3)*sin(n*Pi/3))/6. - Wesley Ivan Hurt, Oct 04 2018