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A002310
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a(n) = 5*a(n-1) - a(n-2).
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4
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1, 2, 9, 43, 206, 987, 4729, 22658, 108561, 520147, 2492174, 11940723, 57211441, 274116482, 1313370969, 6292738363, 30150320846, 144458865867, 692144008489, 3316261176578, 15889161874401, 76129548195427
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Together with A002320 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.: (1-3x)/(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)
a002310 n = a002310_list !! n
a002310_list = 1 : 2 :
(zipWith (-) (map (* 5) (tail a002310_list)) a002310_list)
-- Reinhard Zumkeller, Oct 16 2011
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CROSSREFS
| Cf. A054477.
Sequence in context: A132847 A121365 A018960 * A055728 A006795 A055824
Adjacent sequences: A002307 A002308 A002309 * A002311 A002312 A002313
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KEYWORD
| nonn
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AUTHOR
| Joe Keane (jgk(AT)jgk.org)
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