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A136619
a(1) = 1, then repeat period 3: [1, 4, 2].
1
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, 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, 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
OFFSET
1,3
LINKS
Cayanne McFarlane and Wm. Douglas Withers, Dynamical Systems and Irrational Angle Construction by Paper-Folding, American Mathematical Monthly, Volume 115, Number 4, April 2008, page 356.
FORMULA
G.f.: x*(x^3 + 4*x^2 + x + 1)/(1 - x^3). - Ralf Stephan, Nov 29 2013
a(n) = 2^(-n-1 mod 3) for n>1. - Wesley Ivan Hurt, Feb 21 2015
From Wesley Ivan Hurt, Jul 01 2016: (Start)
a(n) = a(n-3) for n>4.
a(n) = (7 + 5*cos(2*n*Pi/3) + sqrt(3)*sin(2*n*Pi/3))/3 for n>1. (End)
MAPLE
A136619:=n->2^(-n-1 mod 3): (1, seq(A136619(n), n=2..100)); # Wesley Ivan Hurt, Feb 21 2015
MATHEMATICA
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}]
Join[{1}, PadRight[{}, 110, {1, 4, 2}]] (* Bruno Berselli, Nov 30 2013 *)
PROG
(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
(Magma) [1] cat &cat [[1, 4, 2]^^30]; // Wesley Ivan Hurt, Jul 01 2016
CROSSREFS
Sequence in context: A105699 A023526 A082901 * A132708 A153727 A349245
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Mar 31 2008
EXTENSIONS
Edited by Ralf Stephan, Nov 29 2013
STATUS
approved