A233820 Period 4: repeat [20, 5, 15, 10].

20, 5, 15, 10, 20, 5, 15, 10, 20, 5, 15, 10, 20, 5, 15, 10, 20, 5, 15, 10, 20, 5, 15, 10, 20, 5, 15, 10, 20, 5, 15, 10, 20, 5, 15, 10, 20, 5, 15, 10, 20, 5, 15, 10, 20, 5, 15, 10, 20, 5, 15, 10, 20, 5, 15, 10, 20, 5, 15, 10, 20, 5, 15, 10, 20, 5, 15, 10, 20, 5

Offset: 1

Author

Arkadiusz Wesolowski, Dec 16 2013

Keywords

• nonn
• easy

Comments

Clockwise sectors around outside of London Fives dartboard.

Links

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

Crossrefs

Cf. A003833.

Programs

Magma

&cat[[20,5,15,10]: n in [1..17]]; // Bruno Berselli, Dec 16 2013

Maple

seq(op([20, 5, 15, 10]), n=0..50); # Wesley Ivan Hurt, Jul 07 2016

Mathematica

Flatten[Table[{20, 5, 15, 10}, {17}]]

PARI

a(n)=[10,20,5,15][n%4+1] \\ Charles R Greathouse IV, Aug 20 2015

Formula

From Bruno Berselli, Dec 16 2013: (Start)

G.f.: 5*x*(4 + x + 3*x^2 + 2*x^3)/((1 - x)*(1 + x)*(1 + x^2)).

a(n) = 5*(I^(n*(n-1)) - 2*(-1)^n + 5)/2. (End)

From Wesley Ivan Hurt, Jul 07 2016: (Start)

a(n) = 5*(5 + cos(n*Pi/2) - 2*cos(n*Pi) + sin(n*Pi/2) - 2*I*sin(n*Pi))/2.

a(n) = a(n-4) for n>4. (End)