cp's OEIS Frontend

A158068 Period 6: repeat [1, 2, 2, 1, 5, 5].

%I A158068 #19 Dec 12 2023 08:08:24
%S A158068 1,2,2,1,5,5,1,2,2,1,5,5,1,2,2,1,5,5,1,2,2,1,5,5,1,2,2,1,5,5,1,2,2,1,
%T A158068 5,5,1,2,2,1,5,5,1,2,2,1,5,5,1,2,2,1,5,5,1,2,2,1,5,5,1,2,2,1,5,5,1,2,
%U A158068 2,1,5,5,1,2,2,1,5,5,1,2,2,1,5,5,1,2,2,1,5,5,1,2,2,1,5,5,1,2,2,1,5,5,1,2,2
%N A158068 Period 6: repeat [1, 2, 2, 1, 5, 5].
%C A158068 The sequence can be generated starting an array T(n,k) by placing the
%C A158068 periodic sequence 1,2,5 (repeat 1,2,5) in the top row n=0, then defining
%C A158068 the next rows by T(n+1,k) = T(n,k)*T(n,k+1) mod 9, which all have a period T(n,k)=T(n,k+3).
%C A158068 One finds the periodicity T(n+6,k)=T(n,k), and then defines a(n)=T(n,1).
%C A158068 Also the partial fraction expansion of (85+sqrt(12469))/138.
%C A158068 Also the decimal expansion of 11105/90909.
%H A158068 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,1,-1,1).
%F A158068 a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) for n>4.
%F A158068 G.f.: (1+x+5*x^4+x^2)/((1-x)*(1-x+x^2)*(1+x+x^2)). [Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009]
%F A158068 a(n) = (8-5*cos(2*n*Pi/3)-3*sqrt(3)*sin(n*Pi/3))/3. - _Wesley Ivan Hurt_, Jun 17 2016
%p A158068 A158068:=n->(8-5*cos(2*n*Pi/3)-3*sqrt(3)*sin(n*Pi/3))/3: seq(A158068(n), n=0..100); # _Wesley Ivan Hurt_, Jun 17 2016
%t A158068 PadRight[{}, 120, {1,2,2,1,5,5}] (* or *) LinearRecurrence[{1,-1,1,-1,1},{1,2,2,1,5}, 120] (* _Harvey P. Dale_, Jan 27 2015 *)
%o A158068 (Magma) &cat[[1, 2, 2, 1, 5, 5]: n in [0..20]]; // _Wesley Ivan Hurt_, Jun 17 2016
%Y A158068 Cf. A157742, A158012.
%K A158068 nonn,easy
%O A158068 0,2
%A A158068 _Paul Curtz_, Mar 12 2009
%E A158068 Offset set to 0 - _R. J. Mathar_, Sep 17 2009