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a(n) = 3^n mod 30.
1

%I #21 Jan 23 2023 08:49:22

%S 1,3,9,27,21,3,9,27,21,3,9,27,21,3,9,27,21,3,9,27,21,3,9,27,21,3,9,27,

%T 21,3,9,27,21,3,9,27,21,3,9,27,21,3,9,27,21,3,9,27,21,3,9,27,21,3,9,

%U 27,21,3,9,27,21,3,9,27,21,3,9,27,21,3,9,27,21,3,9,27,21,3,9,27,21,3,9,27

%N a(n) = 3^n mod 30.

%H Vincenzo Librandi, <a href="/A168427/b168427.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,1).

%F From _Chai Wah Wu_, Jan 22 2023: (Start)

%F a(n) = a(n-1) - a(n-2) + a(n-3) for n > 3.

%F G.f.: (-20*x^3 - 7*x^2 - 2*x - 1)/((x - 1)*(x^2 + 1)). (End)

%t PowerMod[3,Range[0,90],30] (* _Harvey P. Dale_, Nov 04 2011 *)

%o (Sage) [power_mod(3,n,30) for n in range(0, 88)] #

%o (PARI) a(n)=lift(Mod(3,30)^n) \\ _Charles R Greathouse IV_, Mar 22 2016

%o (Python)

%o def A168427(n): return (21,3,9,27)[n&3] if n else 1 # _Chai Wah Wu_, Jan 22 2023

%Y Cf. A001148.

%K nonn,easy

%O 0,2

%A _Zerinvary Lajos_, Nov 25 2009