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A195617
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Numerators b(n) of Pythagorean approximations b(n)/a(n) to 3.
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4
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35, 1333, 50615, 1922041, 72986939, 2771581645, 105247115567, 3996618809905, 151766267660819, 5763121552301221, 218846852719785575, 8310417281799550633, 315577009855663138475, 11983615957233399711421, 455061829365013525895519
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OFFSET
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1,1
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COMMENTS
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See A195500 for discussion and list of related sequences; see A195616 for Mathematica program.
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LINKS
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FORMULA
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a(n) = 37*a(n-1) + 37*a(n-2) - a(n-3).
G.f.: x*(35+38*x-x^2) / ((1+x)*(1-38*x+x^2)). (End)
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MATHEMATICA
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Table[(3*LucasL[2*n+1, 6] +2*(-1)^n)/20, {n, 40}] (* G. C. Greubel, Feb 13 2023 *)
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PROG
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(PARI) Vec(-x*(x^2-38*x-35)/((x+1)*(x^2-38*x+1)) + O(x^50)) \\ Colin Barker, Jun 04 2015
(Magma) I:=[35, 1333, 50615]; [n le 3 select I[n] else 37*Self(n-1) +37*Self(n-2) -Self(n-3): n in [1..40]]; // G. C. Greubel, Feb 13 2023
(SageMath)
A085447=BinaryRecurrenceSequence(6, 1, 2, 6)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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