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A087619
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a(n) = 137*a(n-1) + a(n-2), with a(0) = 2 and a(1) = 137.
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0
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2, 137, 18771, 2571764, 352350439, 48274581907, 6613970071698, 906162174404533, 124150831863492719, 17009570127472907036, 2330435258295651756651, 319286639956631763568223
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OFFSET
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0,1
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COMMENTS
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a(n+1)/a(n) converges to (137+sqrt(18773))/2 = 137.00729888121410965...
a(0)/a(1) = 2/137;
a(1)/a(2) = 137/18771;
a(2)/a(3) = 18771/2571764;
a(3)/a(4) = 2571764/352350439; ... etc.
Lim_{n->infinity} a(n)/a(n+1) = 0.00729888121410965... = 2/(137+sqrt(18773)) = (sqrt(18773)-137)/2.
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LINKS
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FORMULA
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a(n) = ((137+sqrt(18773))/2)^n + ((137-sqrt(18773))/2)^n.
(a(n))^2 = a(2*n)-2 if n = 1, 3, 5, ..., (a(n))^2 = a(2n) + 2 if n = 2, 4, 6, ...
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CROSSREFS
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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), Oct 25 2003
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STATUS
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approved
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