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A058181
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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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1
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1, 0, -1, 1, 2, 3, 7, 46, 2109, 4447835, 19783236185116, 391376433956083065015485621, 153175513056180249189030531428945090978436751221570525
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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LINKS
| A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fib. Quart., 11 (1973), 429-437.
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>=4, a(n)=ceil(c^(2^n)) with c=1.0303497388742578142745024606710866\
16436302563960998408889321488508667424048981473368773165340730475719244472111...
and c^(1/4)=1.0075025785879710605024343257517358... - Benoit Cloitre, Apr 16 2007
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EXAMPLE
| a(6)=a(5)^2-a(4)=3^2-2=7
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MATHEMATICA
| Join[{a=1, b=0}, Table[c=b^2-a; a=b; b=c, {n, 13}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 18 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. A058182.
Sequence in context: A068393 A032053 A086542 * A198959 A090593 A030090
Adjacent sequences: A058178 A058179 A058180 * A058182 A058183 A058184
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KEYWORD
| sign
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Nov 15 2000
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