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Search: id:A156570
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| A156570 |
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a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1)=17, a(2)=65. |
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4
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| 17, 65, 373, 2173, 12665, 73817, 430237, 2507605, 14615393, 85184753, 496493125, 2893773997, 16866150857, 98303131145, 572952636013, 3339412684933, 19463523473585, 113441728156577, 661186845465877, 3853679344638685
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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lim_{n -> infinity} a(n)/a(n-1) = 3+2*sqrt(2).
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FORMULA
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a(n) = ((74+47*sqrt(2))*(3-2*sqrt(2))^n+(74-47*sqrt(2))*(3+2*sqrt(2))^n)/4.
G.f.: x*(17-37*x)/(1-6*x+x^2).
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PROGRAM
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(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r2>:=NumberField(x^2-2); S:=[ ((74+47*r2)*(3-2*r2)^n+(74-47*r2)*(3+2*r2)^n)/4: n in [1..20] ]; [ Integers()!S[j]: j in [1..#S] ];
(PARI) {m=20; v=concat([17, 65], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-v[n-2]); v}
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CROSSREFS
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First trisection of A156567.
Cf. A156035 (decimal expansion of 3+2*sqrt(2)), A156568, A156569.
Sequence in context: A130885 A036545 A146807 this_sequence A147231 A146815 A044155
Adjacent sequences: A156567 A156568 A156569 this_sequence A156571 A156572 A156573
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Feb 11 2009, Feb 16 2009
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EXTENSIONS
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G.f. corrected by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 22 2009
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