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Search: id:A153886
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| A153886 |
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a(n) = ((9+sqrt(5))^n-(9-sqrt(5))^n)/(2*sqrt(5)). |
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+0
1
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| 1, 18, 248, 3096, 36880, 428544, 4910912, 55827072, 631657984, 7126986240, 80279745536, 903384465408, 10159659716608, 114216655527936, 1283765661040640, 14427316078608384, 162125499175862272
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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lim_{n -> infinity} a(n)/a(n-1) = 9+sqrt(5) = 11.236067977499789696....
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FORMULA
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a(n) = 18*a(n-1)-76*a(n-2) for n>1; a(0)=0, a(1)=1. G.f.: x/(1-18*x+76*x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr) and Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 03 2009]
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PROGRAM
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(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((9+r)^n-(9-r)^n)/(2*r): n in [1..17] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 04 2009]
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CROSSREFS
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Cf. A002163 (decimal expansion of sqrt(5)).
Sequence in context: A153600 A016183 A016239 this_sequence A154241 A154250 A154350
Adjacent sequences: A153883 A153884 A153885 this_sequence A153887 A153888 A153889
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KEYWORD
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nonn
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AUTHOR
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Al Hakanson (hawkuu(AT)gmail.com), Jan 03 2009
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EXTENSIONS
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Extended beyond a(7) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 04 2009
Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 11 2009
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