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Search: id:A000278
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| A000278 |
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a(n) = a(n-1) + a(n-2)^2. |
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+0
10
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| 0, 1, 1, 2, 3, 7, 16, 65, 321, 4546, 107587, 20773703, 11595736272, 431558332068481, 134461531248108526465, 186242594112190847520182173826
(list; graph; listen)
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OFFSET
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0,4
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LINKS
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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
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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 (benoit7848c(AT)orange.fr), May 03 2003
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MAPLE
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A000278 := proc(n) option remember; if n <= 1 then n else A000278(n-2)^2+A000278(n-1); fi; end;
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PROGRAM
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(PARI) a(n)=if(n<2, n>0, a(n-1)+a(n-2)^2)
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CROSSREFS
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Cf. A000283.
Adjacent sequences: A000275 A000276 A000277 this_sequence A000279 A000280 A000281
Sequence in context: A002854 A036356 A034732 this_sequence A077322 A089144 A045332
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KEYWORD
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nonn
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AUTHOR
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greenfie(AT)math.rutgers.edu (Stephen J. Greenfield)
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