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A058181
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Quadratic recurrence a(n) = a(n-1)^2 - a(n-2) for n >= 2 with a(0) = 1 and a(1) = 0.
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2
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1, 0, -1, 1, 2, 3, 7, 46, 2109, 4447835, 19783236185116, 391376433956083065015485621, 153175513056180249189030531428945090978436751221570525
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OFFSET
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0,5
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LINKS
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FORMULA
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a(n)^2 = a(n+1) + a(n-1), a(-1-n) = a(n).
For n >= 4, a(n) = ceiling(c^(2^n)) with c=1.0303497388742578142745024606710866\
16436302563960998408889321488508667424048981473368773165340730475719244472111...
and c^(1/4) = 1.0075025785879710605024343257517358... - Benoit Cloitre, Apr 16 2007
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EXAMPLE
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a(6) = a(5)^2 - a(4) = 3^2 - 2 = 7.
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MATHEMATICA
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RecurrenceTable[{a[0]==1, a[1]==0, a[n]==a[n-1]^2 - a[n-2]}, a, {n, 13}] (* Vincenzo Librandi, Nov 11 2012 *)
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PROG
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(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 */
(Magma) I:=[1, 0]; [n le 2 select I[n] else Self(n-1)^2 - Self(n-2): n in [1..15]]; // G. C. Greubel, Jun 09 2019
(Sage)
def a(n):
if (n==0): return 1
elif (n==1): return 0
else: return a(n-1)^2 - a(n-2)
(GAP) a:=[1, 0];; for n in [3..15] do a[n]:=a[n-1]^2-a[n-2]; od; a; # G. C. Greubel, Jun 09 2019
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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