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Search: id:A156569
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| A156569 |
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a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1)=37, a(2)=205. |
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+0
4
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| 37, 205, 1193, 6953, 40525, 236197, 1376657, 8023745, 46765813, 272571133, 1588660985, 9259394777, 53967707677, 314546851285, 1833313400033, 10685333548913, 62278687893445, 362986793811757, 2115642074977097
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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) = ((34+7*sqrt(2))*(3-2*sqrt(2))^n+(34-7*sqrt(2))*(3+2*sqrt(2))^n)/4.
G.f.: x*(37-17*x)/(1-6*x+x^2).
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PROGRAM
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(PARI) {m=19; v=concat([37, 205], 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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Third trisection of A156567.
Cf. A156035 (decimal expansion of 3+2*sqrt(2)), A156568, A156570.
Sequence in context: A109320 A053872 A141954 this_sequence A141984 A052166 A142010
Adjacent sequences: A156566 A156567 A156568 this_sequence A156570 A156571 A156572
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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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