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Search: id:A154350
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| A154350 |
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a(n) = ((9+2*sqrt(2))^n-(9-2*sqrt(2))^n)/(4*sqrt(2)). |
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+0
1
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| 1, 18, 251, 3204, 39349, 474390, 5666543, 67367304, 798953833, 9463355802, 112016774627, 1325476969740, 15681360907549, 185504677544862, 2194344849556439, 25956365831240976, 307027410944717521
(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+2*sqrt(2) = 11.8284271247....
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FORMULA
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G.f.: x/(1-18*x+73*x^2). [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 12 2009, corrected Oct 08 2009]
a(n) = 18*a(n-1)-73*a(n-2) for n>1; a(0)=0, a(1)=1. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 12 2009]
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PROGRAM
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(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((9+2*r)^n-(9-2*r)^n)/(4*r): n in [1..17] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 12 2009]
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CROSSREFS
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Cf. A002193 (decimal expansion of sqrt(2)).
Sequence in context: A153886 A154241 A154250 this_sequence A001722 A060788 A144708
Adjacent sequences: A154347 A154348 A154349 this_sequence A154351 A154352 A154353
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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 07 2009
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EXTENSIONS
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Extended beyond a(7) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 12 2009
Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 08 2009
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