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A058182
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Quadratic recurrence a(n)=a(n-1)^2+a(n-2), a(0)=1,a(1)=0.
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4
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1, 0, 1, 1, 2, 5, 27, 734, 538783, 290287121823, 84266613096281243382112, 7100862082718357559748563880517486086728702367, 50422242317787290639189291009890702507917377925161079229314384058371278254659634544914784801
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| 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
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LINKS
| N. J. A. Sloane, Transforms
Index entries for sequences of form a(n+1)=a(n)^2 + ...
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FORMULA
| 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
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EXAMPLE
| a(6)=a(5)^2+a(4)=5^2+2=27
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MATHEMATICA
| Join[{a=1, b=0}, Table[c=a+b^2; a=b; b=c, {n, 12}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 22 2011*)
Join[{1}, Transpose[NestList[{Last[#], Last[#]^2+First[#]}&, {0, 1}, 12]][[1]]] (* From Harvey P. Dale, May 15 2011 *)
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PROG
| (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 */
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CROSSREFS
| Cf. A000278, A005605, A058181.
Sequence in context: A079716 A203195 A207324 * A057438 A002795 A127357
Adjacent sequences: A058179 A058180 A058181 * A058183 A058184 A058185
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KEYWORD
| nonn,nice,eigen
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Nov 15 2000
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EXTENSIONS
| More terms from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 16 2006
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