A131598 - OEIS

%I #52 Dec 12 2023 09:18:52

%S 2,5,8,2,5,8,2,5,8,2,5,8,2,5,8,2,5,8,2,5,8,2,5,8,2,5,8,2,5,8,2,5,8,2,

%T 5,8,2,5,8,2,5,8,2,5,8,2,5,8,2,5,8,2,5,8,2,5,8,2,5,8,2,5,8,2,5,8,2,5,

%U 8,2,5,8,2,5,8,2,5,8,2,5,8,2,5,8,2,5,8,2,5,8,2,5,8,2,5,8,2,5,8,2,5,8,2,5,8

%N Period 3: repeat [2, 5, 8].

%C From _Klaus Brockhaus_, May 16 2010: (Start)

%C Continued fraction expansion of (85+sqrt(9029))/82.

%C Decimal expansion of 86/333. (End)

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).

%F a(n) = 5 - 3*cos(2/3*Pi*n) - 3^(1/2)*sin(2/3*Pi*n). - _R. J. Mathar_, Nov 15 2007

%F G.f.: (2+5*x+8*x^2)/(1-x^3). - _Jaume Oliver Lafont_, Mar 24 2009

%F a(n) = a(n-3) for n>2. - _Wesley Ivan Hurt_, Jul 01 2016

%F a(n) = 3*(n mod 3) + 2, see PARI code. - _Bruno Berselli_, Jul 25 2018

%F E.g.f.: 5*exp(x) - exp(-x/2)*(3*cos(sqrt(3)*x/2) + sqrt(3)*sin(sqrt(3)*x/2)). - _Stefano Spezia_, Sep 11 2022

%p seq(op([2, 5, 8]), n=0..50); # _Wesley Ivan Hurt_, Jul 01 2016

%t PadRight[{}, 120, {2,5,8}] (* _Harvey P. Dale_, Jun 22 2013 *)

%t Table[3 Mod[n, 3] + 2, {n, 0, 120}] (* or *)

%t CoefficientList[Series[(2 + 5 x + 8 x^2)/(1 - x^3), {x, 0, 120}], x]  (* _Michael De Vlieger_, Jul 02 2016 *)

%o (PARI) a(n)=2+3*(n%3) \\ _Jaume Oliver Lafont_, Mar 24 2009

%o (Magma) &cat [[2, 5, 8]^^30]; // _Wesley Ivan Hurt_, Jul 01 2016

%Y Cf. A177972 (decimal expansion of (85+sqrt(9029))/82).

%K nonn,easy

%O 0,1

%A _Paul Curtz_, Oct 02 2007