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Search: id:A131216
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| A131216 |
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Numbers X such that 99*X^2-2178 is a square. |
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| 11, 209, 4169, 83171, 1659251, 33101849, 660377729, 13174452731, 262828676891, 5243399085089, 104605153024889, 2086859661412691, 41632588075228931, 830564901843165929, 16569665448788089649, 330562744073918627051
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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a(n+2)=20*a(n+1)-a(n) a(n+1)=10*a(n+1)+(99*a(n)^2-2178)^0.5
G.f.: f(z)=a(1)*z+a(2)*z^2+...=(11*z-11*z^2)/(1-20*z+z^2) - R. Choulet (richardchoulet(AT)yahoo.fr), Oct 09 2007
a(n)=(3/2)*[10+3*sqrt(11)]^(n-1)*sqrt(11)+(11/2)*[10+3*sqrt(11)]^(n-1)-(3/2)*sqrt(11)*[10-3 *sqrt(11)]^(n-1)+(11/2)*[10-3*sqrt(11)]^(n-1), with n>=1 - Paolo P. Lava (ppl(AT)spl.at), Jul 15 2008
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CROSSREFS
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Cf. A083043.
Adjacent sequences: A131213 A131214 A131215 this_sequence A131217 A131218 A131219
Sequence in context: A064748 A091814 A020518 this_sequence A034909 A081788 A060496
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KEYWORD
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nonn
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AUTHOR
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Richard Choulet (richardchoulet(AT)yahoo.fr), Sep 27 2007
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