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Search: id:A154248
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| A154248 |
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a(n) = ((7+sqrt(7))^n-(7-sqrt(7))^n)/(2*sqrt(7)). |
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+0
1
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| 1, 14, 154, 1568, 15484, 150920, 1462552, 14137088, 136492048, 1317130976, 12707167648, 122580846080, 1182430803904, 11405635719296, 110016806306176, 1061198588076032, 10236074368205056, 98734700455677440
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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) = 7+sqrt(7) = 9.6457513110....
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FORMULA
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a(n) = 14*a(n-1)-42*a(n-2) for n>1; a(0)=0, a(1)=1. G.f.: x/(1-14x+42x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 06 2009]
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PROGRAM
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(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-7); S:=[ ((7+r)^n-(7-r)^n)/(2*r): n in [1..18] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 07 2009]
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CROSSREFS
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Cf. A010465 (decimal expansion of square root of 7).
Sequence in context: A097227 A125426 A004986 this_sequence A006865 A154347 A001707
Adjacent sequences: A154245 A154246 A154247 this_sequence A154249 A154250 A154251
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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 05 2009
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EXTENSIONS
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Extended beyond a(7) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 07 2009
Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 06 2009
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