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Search: id:A153596
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| A153596 |
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a(n) = ((5+sqrt(3))^n-(5-sqrt(3))^n)/(2*sqrt(3)). |
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+0
2
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| 1, 10, 78, 560, 3884, 26520, 179752, 1214080, 8186256, 55152800, 371430368, 2500942080, 16837952704, 113358801280, 763153053312, 5137636904960, 34587001876736, 232842006858240, 1567506027294208, 10552536122060800
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Third binomial transform of A054485. Fifth binomial transform of A162813 preceded by 1.
lim_{n -> infinity} a(n)/a(n-1) = 5+sqrt(3) = 6.73205080756887729....
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FORMULA
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G.f.: x/(1-10*x+22*x^2). [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 31 2008, corrected Oct 11 2009]
a(n) = 10*a(n-1)-22*a(n-2) for n>1; a(0)=0, a(1)=1. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 01 2009]
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PROGRAM
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(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((5+r)^n-(5-r)^n)/(2*r): n in [1..20] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 31 2008]
(Other) Sage: [lucas_number1(n, 10, 22) for n in xrange(1, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2009]
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CROSSREFS
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Cf. A002194 (decimal expansion of sqrt(3)), A054485, A162813.
Sequence in context: A016201 A080618 A082136 this_sequence A056986 A006469 A081905
Adjacent sequences: A153593 A153594 A153595 this_sequence A153597 A153598 A153599
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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), Dec 29 2008
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EXTENSIONS
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Extended beyond a(7) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 31 2008
Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 11 2009
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