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A000278
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a(n) = a(n-1) + a(n-2)^2 for n >= 2 with a(0) = 0 and a(1) = 1.
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17
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0, 1, 1, 2, 3, 7, 16, 65, 321, 4546, 107587, 20773703, 11595736272, 431558332068481, 134461531248108526465, 186242594112190847520182173826, 18079903385772308300945867582153787570051, 34686303861638264961101080464895364211215702792496667048327
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OFFSET
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0,4
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LINKS
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FORMULA
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a(2n) is asymptotic to A^(sqrt(2)^(2n-1)) where A=1.668751581493687393311628852632911281060730869124873165099170786836201970866312366402366761987... and a(2n+1) to B^(sqrt(2)^(2n)) where B=1.693060557587684004961387955790151505861127759176717820241560622552858106116817244440438308887... See reference for proof. - Benoit Cloitre, May 03 2003
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MAPLE
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MATHEMATICA
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RecurrenceTable[{a[n +2] == a[n +1] + a[n]^2, a[0] == 1, a[1] == 1}, a, {n, 0, 16}] (* Robert G. Wilson v, Apr 14 2017 *)
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PROG
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(PARI) a(n)=if(n<2, n>0, a(n-1)+a(n-2)^2)
(Sage)
x, y = 0, 1
while True:
yield x
x, y = x + y, x * x
(Magma) [n le 2 select n-1 else Self(n-1) + Self(n-2)^2: n in [1..18]]; // Vincenzo Librandi, Dec 17 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Stephen J. Greenfield (greenfie(AT)math.rutgers.edu)
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EXTENSIONS
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STATUS
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approved
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