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Search: id:A002310
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| A002310 |
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a(n) = 5*a(n-1) - a(n-2). |
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+0
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; listen)
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OFFSET
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0,2
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COMMENT
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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
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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.: (1-3x)/(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 (ppl(AT)spl.at), Nov 21 2008]
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CROSSREFS
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Adjacent sequences: A002307 A002308 A002309 this_sequence A002311 A002312 A002313
Sequence in context: A132847 A121365 A018960 this_sequence A055728 A006795 A055824
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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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