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A002320
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a(n) = 5*a(n-1) - a(n-2).
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
| 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
| Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Tanya Khovanova, Recursive Sequences
MathPages, N = (x^2 + y^2)/(1+xy) is a Square
Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
| 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 (paoloplava(AT)gmail.com), Nov 21 2008]
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PROG
| (Haskel)
a002320 n = a002320_list !! n
a002320_list = 1 : 3 :
(zipWith (-) (map (* 5) (tail a002320_list)) a002320_list)
-- Reinhard Zumkeller, Oct 16 2011
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CROSSREFS
| Cf. A054477.
Sequence in context: A026592 A034275 A151322 * A151323 A181662 A113140
Adjacent sequences: A002317 A002318 A002319 * A002321 A002322 A002323
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KEYWORD
| nonn
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AUTHOR
| Joe Keane (jgk(AT)jgk.org)
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