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A000278
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a(n) = a(n-1) + a(n-2)^2.
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11
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0, 1, 1, 2, 3, 7, 16, 65, 321, 4546, 107587, 20773703, 11595736272, 431558332068481, 134461531248108526465, 186242594112190847520182173826
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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LINKS
| W. Duke, Stephen J. Greenfield and Eugene R. Speer, Properties of a Quadratic Fibonacci Recurrence, J. Integer Sequences, 1998, #98.1.8.
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FORMULA
| 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 (benoit7848c(AT)orange.fr), May 03 2003
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MAPLE
| A000278 := proc(n) option remember; if n <= 1 then n else A000278(n-2)^2+A000278(n-1); fi; end;
a[ -2]:=0: a[ -1]:=1:a[0]:=1: a[1]:=2: for n from 2 to 13 do a[n]:=a[n-1]+a[n-2]^2 od: seq(a[n], n=-2..13); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 19 2009]
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MATHEMATICA
| Join[{a=0, b=1}, Table[c=a^2+b; a=b; b=c, {n, 16}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 22 2011*)
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PROG
| (PARI) a(n)=if(n<2, n>0, a(n-1)+a(n-2)^2)
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CROSSREFS
| Cf. A000283.
Sequence in context: A002854 A036356 A034732 * A153787 A141795 A077322
Adjacent sequences: A000275 A000276 A000277 * A000279 A000280 A000281
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KEYWORD
| nonn
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AUTHOR
| greenfie(AT)math.rutgers.edu (Stephen J. Greenfield)
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