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Search: id:A002320
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| A002320 |
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a(n) = 5*a(n-1) - a(n-2). |
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+0
5
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| 1, 3, 14, 67, 321, 1538, 7369, 35307, 169166, 810523, 3883449, 18606722, 89150161, 427144083, 2046570254, 9805707187, 46981965681, 225104121218, 1078538640409, 5167589080827, 24759406763726, 118629444737803
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Together with A002310 these are the two sequences satisfying ( a(n)^2+a(n-1)^2 )/(1 - a(n)a(n-1)) is an integer, in both cases this integer is -5. - Floor van Lamoen (fvlamoen(AT)hotmail.com), Oct 26 2001
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REFERENCES
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From a posting to Netnews group sci.math by ksbrown(AT)seanet.com (K. S. Brown) on Aug 15 1996.
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LINKS
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Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
MathPages, N = (x^2 + y^2)/(1+xy) is a Square
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FORMULA
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Sequences A002310, A002320 and A049685 have this in common: each one satisfies a(n+1) = (a(n)^2+5)/a(n-1) - Graeme McRae (g_m(AT)mcraefamily.com), Jan 30 2005
G.f.: (1-2x)/(1-5x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 16 2008]
a(n)=-(1/42)*sqrt(21)*[(5/2)-(1/2)*sqrt(21)]^n+(1/42)*[(5/2)+(1/2)*sqrt(21)]^n*sqrt(21)+(1/2)*[(5/2) +(1/2)*sqrt(21)]^n+(1/2)*[(5/2)-(1/2)*sqrt(21)]^n, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Nov 21 2008]
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CROSSREFS
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Adjacent sequences: A002317 A002318 A002319 this_sequence A002321 A002322 A002323
Sequence in context: A026592 A034275 A151322 this_sequence A151323 A113140 A151324
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KEYWORD
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nonn
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AUTHOR
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Joe Keane (jgk(AT)jgk.org)
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