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A156160
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a(n) = 34*a(n-1)-a(n-2)-2312 for n > 2; a(1)=169, a(2)=2809.
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2
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169, 2809, 93025, 3157729, 107267449, 3643933225, 123786459889, 4205095700689, 142849467361225, 4852676794578649, 164848161548310529, 5599984815847977025, 190234635577282906009, 6462377624811770824969
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OFFSET
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1,1
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COMMENTS
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lim_{n -> infinity} a(n)/a(n-1) = (17+12*sqrt(2)).
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LINKS
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FORMULA
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a(n) = (578+ (2211-1550*sqrt(2))*(17+12*sqrt(2))^n+(2211+1550*sqrt(2))*(17-12*sqrt(2))^n)/8.
G.f.: x*(169-3106*x+625*x^2)/((1-x)*(1-34*x+x^2)).
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EXAMPLE
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a(3) = 34*a(2)-a(1)-2312 = 34*2809-169-2312 = 93025.
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MATHEMATICA
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LinearRecurrence[{35, -35, 1}, {169, 2809, 93025}, 20] (* Harvey P. Dale, Nov 15 2014 *)
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PROG
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(PARI) {m=14; v=concat([169, 2809], vector(m-2)); for(n=3, m, v[n]=34*v[n-1]-v[n-2]-2312); v}
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CROSSREFS
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Cf. A156164 (decimal expansion of (17+12*sqrt(2))).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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