A005605 a(n) = a(n-1) + (-1)^(n-1) * a(n-2)^2 for n >= 2 with a(0) = 0 and a(1) = 1. (Formerly M0176)

0, 1, 1, 2, 1, 5, 4, 29, 13, 854, 685, 730001, 260776, 532901720777, 464897598601, 283984244007552571082330, 67854466822576053925129, 80647050844541158378200602801460469923692154029

Offset

0,4

References

J. Mestel, Archimedeans Problems Drive 1977, Eureka, 39 (1978), 38-40.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..25

J. Mestel, Archimedeans Problems Drive 1977, Eureka, 39 (1978), 38-40. (Annotated scanned copy)

Formula

For odd n, a(n) = floor(c^(2^((n-5)/2))) where c = 5.40649051189479721671529024151000148043062587729806430849172463824709059699198634362266484243.... - Gerald McGarvey, Dec 08 2004

The alternating version of this sequence, b(n) = (-1)^(n-1)*a(n) = 0,1,-1,2,-1,5,-4,29,-13,..., satisfies b(n) = b(n-2)^2 - b(n-1). - Franklin T. Adams-Watters, Feb 27 2007

Mathematica

t = {0, 1}; Do[AppendTo[t, t[[-2]]^2 - t[[-1]]], {n, 18}]; Abs[t] (* Vladimir Joseph Stephan Orlovsky, Feb 23 2012 *)
nxt[{n_, a1_, a2_}]:={n+1, a2, a2+(-1)^n*a1^2}; Drop[Transpose[NestList[nxt, {0, 0, 1}, 20]][[3]], 2] (* Harvey P. Dale, Oct 03 2012 *)

Prog

(Haskell)
a005605 n = a005605_list !! n
a005605_list = 0 : 1 : zipWith (+) (tail a005605_list)
   (zipWith (*) (cycle [-1, 1]) (map (^ 2) $ a005605_list))
-- Reinhard Zumkeller, Feb 16 2012

Crossrefs

Sequence in context: A124660 A217104 A141485 * A300661 A145882 A209765

Adjacent sequences: A005602 A005603 A005604 * A005606 A005607 A005608

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved