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Search: id:A072877
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| A072877 |
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a(1)=a(2)=a(3)=a(4)=1; a(n)=(a(n-1)a(n-3)+a(n-2)^3)/a(n-4). |
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2
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| 1, 1, 1, 1, 2, 3, 19, 119, 65339, 67258454, 959259994615659593, 171965197021698738644442682357, 12959040525296547835480490169418622922155526267774117749963303914461
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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A generalized Somos-4 sequence with a(n-2)^4 in place of a(n-2)^2.
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REFERENCES
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S. Fomin and A. Zelevinsky, The Laurent Phenomenon, Adv. Appl. Math. 28 (2002) 119-144.
D. Gale, The strange and surprising saga of the Somos sequences, Mathematical Intelligencer 13 (1) (1991), 40-42.
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FORMULA
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The limit of (log(log(a(n))))/n as n tends to infinity is log(2+sqrt(3)) or about 0.658. - Andrew Hone (anwh(AT)kent.ac.uk), Nov 15 2005
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MAPLE
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L[0]:=0; L[1]:=0; L[2]:=0; L[3]:=0; for n from 0 to 4000 do L[n+4]:=evalf(ln(1+exp(L[n+3]+L[n+1]-4*L[n+2]))+4*L[n+2]-L[n]): od: for n from 3990 to 4000 do print(evalf(ln(L[n+4])/(n+4))): od: #Note: L[n] is log(a[n]) (Hone)
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CROSSREFS
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Cf. A006720.
Sequence in context: A009178 A141508 A119344 this_sequence A032329 A066227 A061490
Adjacent sequences: A072874 A072875 A072876 this_sequence A072878 A072879 A072880
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jul 28 2002
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