A158001 Period 6: repeat [9, 10, 9, 4, 4, 1].
9, 10, 9, 4, 4, 1, 9, 10, 9, 4, 4, 1, 9, 10, 9, 4, 4, 1, 9, 10, 9, 4, 4, 1, 9, 10, 9, 4, 4, 1, 9, 10, 9, 4, 4, 1, 9, 10, 9, 4, 4, 1, 9, 10, 9, 4, 4, 1, 9, 10, 9, 4, 4, 1, 9, 10, 9, 4, 4, 1, 9, 10, 9, 4, 4, 1, 9, 10, 9, 4, 4, 1, 9, 10, 9, 4, 4, 1, 9, 10, 9, 4, 4, 1, 9, 10, 9, 4, 4, 1, 9, 10, 9, 4, 4, 1
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).
Programs
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Magma
&cat[[9, 10, 9, 4, 4, 1]^^20]; // Wesley Ivan Hurt, Jun 18 2016
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Maple
A158001:=n->[9, 10, 9, 4, 4, 1][(n mod 6)+1]: seq(A158001(n), n=0..100); # Wesley Ivan Hurt, Jun 18 2016
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Mathematica
Flatten[Table[{9, 10, 9, 4, 4, 1}, {20}]] (* Wesley Ivan Hurt, Jun 18 2016 *) PadRight[{}, 100, {9, 10, 9, 4, 4, 1}] (* Vincenzo Librandi, Jun 19 2016 *)
Formula
From Wesley Ivan Hurt, Jun 18 2016: (Start)
G.f.: x*(9+10*x+9*x^2+4*x^3+4*x^4+x^5)/(1-x^6).
a(n) = a(n-6) for n > 6.
a(n) = (37 - 7*cos(n*Pi) - 17*cos(n*Pi/3) - 7*cos(2*n*Pi/3) + 11*sqrt(3)*sin(n*Pi/3) - sqrt(3)*sin(2*n*Pi/3))/6. (End)