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A164360 Period 3: repeat [5, 4, 3].

%I A164360 #20 Dec 12 2023 08:09:41
%S A164360 5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,
%T A164360 4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,
%U A164360 3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3
%N A164360 Period 3: repeat [5, 4, 3].
%C A164360 From _Klaus Brockhaus_, May 29 2010: (Start)
%C A164360 Continued fraction expansion of (32+sqrt(1297))/13.
%C A164360 Decimal expansion of 181/333. (End)
%H A164360 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).
%F A164360 a(n) = 4+(-1)^n*((1/2+I*sqrt(3)/6)*((1+I*sqrt(3))/2)^n+(1/2-I*sqrt(3)/6)*((1-I*sqrt(3))/2)^n). [Corrected by _Klaus Brockhaus_, Sep 17 2009]
%F A164360 a(n) = 4+(1/3)*sqrt(3)*sin(2*n*Pi/3)+cos(2*n*Pi/3). [Corrected by _Klaus Brockhaus_, Sep 17 2009]
%F A164360 a(n) = a(n-3) for n > 2, with a(0) = 5, a(1) = 4, a(2) = 3.
%F A164360 G.f.: (5+4*x+3*x^2)/((1-x)*(1+x+x^2)). [_Klaus Brockhaus_, Sep 17 2009]
%F A164360 E.g.f.: 4*exp(x)+(1/3)*sqrt(3)*exp(-(1/2)*x)*sin((1/2)*x*sqrt(3))+exp(-(1/2)*x)*cos((1/2)*x*sqrt(3)).
%F A164360 a(n) = 4 + A057078(n). - _Wesley Ivan Hurt_, Jul 01 2016
%p A164360 seq(op([5, 4, 3]), n=0..50); # _Wesley Ivan Hurt_, Jul 01 2016
%t A164360 PadRight[{}, 100, {5, 4, 3}] (* _Wesley Ivan Hurt_, Jul 01 2016 *)
%o A164360 (Magma) [ n le 3 select 6-n else Self(n-3):n in [1..105] ]; // _Klaus Brockhaus_, Sep 17 2009
%o A164360 (Magma) &cat [[5, 4, 3]^^30]; // _Wesley Ivan Hurt_, Jul 01 2016
%Y A164360 Cf. A007877 (repeat 0,1,2,1), A068073 (repeat 1,2,3,2), A028356 (repeat 1,2,3,4,3,2), A130784 (repeat 1,3,2), A158289 (repeat 0,1,2,3,4,5,6,7,8,9,8,7,6,5,4,3,2,1).
%Y A164360 Cf. A178566 (decimal expansion of (32+sqrt(1297))/13). [_Klaus Brockhaus_, May 29 2010]
%K A164360 easy,nonn
%O A164360 0,1
%A A164360 _Stephen Crowley_, Aug 14 2009
%E A164360 Edited by _Klaus Brockhaus_, Sep 17 2009
%E A164360 Offset changed to 0 and formulas adjusted by _Klaus Brockhaus_, May 18 2010