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A156162
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a(n) = 34*a(n-1)-a(n-2)-2312 for n > 2; a(1)=625, a(2)=18769.
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2
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625, 18769, 635209, 21576025, 732947329, 24898630849, 845820499225, 28732998340489, 976076123075089, 33157855186210225, 1126391000208070249, 38264136151888175929, 1299854238163989909025, 44156779961423768728609
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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+(387-182*sqrt(2))*(17+12*sqrt(2))^n+(387+182*sqrt(2))*(17-12*sqrt(2))^n)/8.
G.f.: x*(625-3106*x+169*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*18769-625-2312 = 635209.
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MATHEMATICA
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RecurrenceTable[{a[1]==625, a[2]==18769, a[n]==34a[n-1]-a[n-2]-2312}, a, {n, 20}] (* or *) LinearRecurrence[{35, -35, 1}, {625, 18769, 635209}, 20] (* Harvey P. Dale, Sep 29 2016 *)
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PROG
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(PARI) {m=14; v=concat([625 , 18769], 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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