A070347 - OEIS

%I #35 Dec 25 2023 13:46:47

%S 1,2,4,8,16,11,1,2,4,8,16,11,1,2,4,8,16,11,1,2,4,8,16,11,1,2,4,8,16,

%T 11,1,2,4,8,16,11,1,2,4,8,16,11,1,2,4,8,16,11,1,2,4,8,16,11,1,2,4,8,

%U 16,11,1,2,4,8,16,11,1,2,4,8,16,11,1,2,4,8,16,11,1,2,4,8,16,11,1,2,4,8,16,11

%N a(n) = 2^n mod 21.

%H G. C. Greubel, <a href="/A070347/b070347.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,1,-1,1).

%F From _R. J. Mathar_, Apr 13 2010: (Start)

%F a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5).

%F G.f.: (1 + x + 3*x^2 + 5*x^3 + 11*x^4)/ ((1-x) * (1+x+x^2) * (1-x+x^2)). (End)

%F a(n) = a(n-6). - _G. C. Greubel_, Mar 11 2016

%t PowerMod[2, Range[0, 50], 21] (* _G. C. Greubel_, Mar 11 2016 *)

%t LinearRecurrence[{1,-1,1,-1,1},{1,2,4,8,16},120] (* or *) PadRight[{},120,{1,2,4,8,16,11}] (* _Harvey P. Dale_, Mar 19 2016 *)

%o (Sage) [power_mod(2,n,21)for n in range(0,90)] # _Zerinvary Lajos_, Nov 03 2009

%o (PARI) a(n)=lift(Mod(2,21)^n) \\ _Charles R Greathouse IV_, Mar 22 2016

%o (GAP) List([0..83],n->PowerMod(2,n,21)); # _Muniru A Asiru_, Jan 31 2019

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, May 12 2002