A136619 a(1) = 1, then repeat period 3: [1, 4, 2].

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

Table of n, a(n) for n=1..102.

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.

Index entries for linear recurrences with constant coefficients, signature (0,0,1).

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

Adjacent sequences: A136616 A136617 A136618 * A136620 A136621 A136622

Keyword

nonn,easy

Author

Roger L. Bagula, Mar 31 2008

Extensions

Edited by Ralf Stephan, Nov 29 2013

Status

approved