0,5

Has property that CONTINUANT([1, 1, 2, 5, 27, 734, 538783, ...]) = [1, 2, 5, 27, 734, 538783, ...]. - N. J. A. Sloane (njas(AT)research.att.com) Jul 19 2002

N. J. A. Sloane, Transforms

Index entries for sequences of form a(n+1)=a(n)^2 + ...

a(n)^2=a(n+1)-a(n-1), a(-1-n)=-a(n).

For n>1, a(n+1) = floor(c^(2^n)) where c=1.108604586393628626769904017539.... - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 30 2002

a(n+1) = a(n)^2+floor(sqrt(a(n))) = A000290(a(n))+A000196(a(n)) for n>2. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 16 2006

a(6)=a(5)^2+a(4)=5^2+2=27

a[ -2]:=1: a[ -1]:=0:a[0]:=1: a[1]:=2: for n from 2 to 13 do a[n]:=a[n-1]^2+a[n-2] od: seq(a[n], n=-2..9); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 19 2009]

(PARI) a(n)=if(n<0, -a(-1-n), if(n<2, 1-n, a(n-1)^2+a(n-2))) /* Michael Somos May 05 2005 */

Cf. A000278, A005605, A058181.

Sequence in context: A087130 A097565 A079716 this_sequence A057438 A002795 A127357

Adjacent sequences: A058179 A058180 A058181 this_sequence A058183 A058184 A058185

nonn,nice,eigen

Henry Bottomley (se16(AT)btinternet.com), Nov 15 2000

More terms from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 16 2006