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%I #40 Dec 12 2023 08:42:46
%S 1,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,
%T 1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,
%U 4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4,2,1,4
%N a(1) = 1, then repeat period 3: [1, 4, 2].
%H Cayanne McFarlane and Wm. Douglas Withers, <a href="http://www.jstor.org/stable/27642479">Dynamical Systems and Irrational Angle Construction by Paper-Folding</a>, American Mathematical Monthly, Volume 115, Number 4, April 2008, page 356.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).
%F G.f.: x*(x^3 + 4*x^2 + x + 1)/(1 - x^3). - _Ralf Stephan_, Nov 29 2013
%F a(n) = 2^(-n-1 mod 3) for n>1. - _Wesley Ivan Hurt_, Feb 21 2015
%F From _Wesley Ivan Hurt_, Jul 01 2016: (Start)
%F a(n) = a(n-3) for n>4.
%F a(n) = (7 + 5*cos(2*n*Pi/3) + sqrt(3)*sin(2*n*Pi/3))/3 for n>1. (End)
%p A136619:=n->2^(-n-1 mod 3): (1,seq(A136619(n), n=2..100)); # _Wesley Ivan Hurt_, Feb 21 2015
%t Clear[A, m, n]; m = 3; A[0] = 1; A[1] = (m - 1)/2; A[n_] := A[n] = If[Mod[A[n - 1], 2] == 0, A[n - 1]/2, (m - A[n - 1]) 2]; Table[A[n], {n, 0, 110}]
%t Join[{1}, PadRight[{}, 110, {1, 4, 2}]] (* _Bruno Berselli_, Nov 30 2013 *)
%o (PARI) lista(nn) = {m = 3; a = 1; print1(a, ", "); a = (m - 1)/2; print1(a, ", "); for (n=2, nn, print1(a, ", "); if ((a % 2) == 0, a = a/2, a = 2*(m-a)););} \\ _Michel Marcus_, Nov 30 2013
%o (Magma) [1] cat &cat [[1, 4, 2]^^30]; // _Wesley Ivan Hurt_, Jul 01 2016
%K nonn,easy
%O 1,3
%A _Roger L. Bagula_, Mar 31 2008
%E Edited by _Ralf Stephan_, Nov 29 2013
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