A168427 a(n) = 3^n mod 30.

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, 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, 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

Offset: 0

Author

Zerinvary Lajos, Nov 25 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,-1,1).

Crossrefs

Cf. A001148.

Programs

Mathematica

PowerMod[3,Range[0,90],30] (* Harvey P. Dale, Nov 04 2011 *)

PARI

a(n)=lift(Mod(3,30)^n) \\ Charles R Greathouse IV, Mar 22 2016

Python

def A168427(n): return (21,3,9,27)[n&3] if n else 1 # Chai Wah Wu, Jan 22 2023

Sage

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

Formula

From Chai Wah Wu, Jan 22 2023: (Start)

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

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