A136615 Fold-switch-fold sequence defined by McFarlane and Withers for m=3: Let A(n) = If[Mod[A(n - 1), 2] == 0, A(n - 1)/2, (m - A(n - 1))2]; a(n)= If[ Mod[A(n - 1), 2] == 0, a(n - 1)/2, (Pi - a(n - 1))/2].

1, 2, 0, 0, 0, 16, 16, 16, 112, 112, 112, 912, 912, 912, 7280, 7280, 7280, 58256, 58256, 58256, 466032, 466032, 466032, 3728272, 3728272, 3728272, 29826160, 29826160, 29826160, 238609296, 238609296, 238609296, 1908874352, 1908874352

Offset

1,2

References

Cayanne McFarlane and Wm. Douglas Withers; Dynamical Systems and Irrational Angle Construction by Paper-Folding, American Mathematical Monthly, Volume 115, Number 4, 2008, page 356; http://www.maa.org/pubs/monthly_apr08_toc.html.

Links

Table of n, a(n) for n=1..34.

Formula

m=3,A(0)=1;a(1)=(m-1)/2; A(n) = If[Mod[A(n - 1), 2] == 0, A(n - 1)/2, (m - A(n - 1))2]; a(0) = Pi; a(1) = Pi; a(n)= If[ Mod[A(n - 1), 2] == 0, a(n - 1)/2, (Pi - a(n - 1))/2]; output=2^n*a(n)/Pi

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]; a[0] = Pi; a[1] = Pi; a[n_] := a[n] = If[ Mod[A[n - 1], 2] == 0, a[n - 1]/2, (Pi - a[n - 1])/2]; Table[2^n*a[n]/Pi, {n, 0, 50}]

Crossrefs

Sequence in context: A250397 A348029 A224074 * A283950 A342376 A277443

Adjacent sequences: A136612 A136613 A136614 * A136616 A136617 A136618

Keyword

nonn

Author

Roger L. Bagula, Mar 31 2008

Status

approved