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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)
4
0, 1, 1, 2, 1, 5, 4, 29, 13, 854, 685, 730001, 260776, 532901720777, 464897598601, 283984244007552571082330, 67854466822576053925129, 80647050844541158378200602801460469923692154029 (list; graph; refs; listen; history; text; internal format)
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,changed

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 13 04:20 EST 2019. Contains 329085 sequences. (Running on oeis4.)