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Search: id:A089775
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| 2, 322, 103682, 33385282, 10749957122, 3461452808002, 1114577054219522, 358890350005878082, 115561578124838522882, 37210469265847998489922, 11981655542024930675232002
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OFFSET
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0,1
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COMMENT
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a(n+1)/a(n) converges to (322+sqrt(103680))/2 = 321,996894379... a(0)/a(1)=2/322; a(1)/a(2)= 322/103682; a(2)/a(3)= 103682/33385282; a(3)/a(4)= 33385282/10749957122; ... etc. Lim a(n)/a(n+1) as n approaches infinity = 0.00310562... = 2/(322+sqrt(103680)) = (322-sqrt(103680))/2.
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LINKS
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Tanya Khovanova, Recursive Sequences
Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)
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FORMULA
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a(n) =322a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 322, a(n) = ((322+sqrt(103680))/2)^n + ((322-sqrt(103680))/2)^n, (a(n))^2 =a(2n)+2.
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EXAMPLE
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a(4) =10749957122 = 322a(3) - a(2) = 322*33385282 - 103682=((322+sqrt(103680))/2)^4 + ((322-sqrt(103680))/2)^4 =10749957121,999999999906976373 + 0.000000000093023626 = 10749957122.
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CROSSREFS
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Cf. A000032, A060964.
a(n) = A000032(12n).
Sequence in context: A119779 A118579 A062205 this_sequence A094402 A028483 A006475
Adjacent sequences: A089772 A089773 A089774 this_sequence A089776 A089777 A089778
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KEYWORD
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easy,nonn
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AUTHOR
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Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Jan 09 2004
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