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A195623
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Numerators of Pythagorean approximations to 5.
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4
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99, 10101, 1030199, 105070201, 10716130299, 1092940220301, 111469186340399, 11368764066500401, 1159502465596700499, 118257882726796950501, 12061144535667692250599, 1230118484755377812610601, 125460024300512869194030699
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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 A195622 for Mathematica program.
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LINKS
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FORMULA
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a(n) = 101*a(n-1) + 101*a(n-2) - a(n-3).
G.f.: x*(99+102*x-x^2)/((1+x)*(1-102*x+x^2)). (End)
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MATHEMATICA
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Table[(5*LucasL[2*n+1, 10] +2*(-1)^n)/52, {n, 40}] (* G. C. Greubel, Feb 16 2023 *)
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PROG
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(PARI) Vec(-x*(x^2-102*x-99) / ((x+1)*(x^2-102*x+1)) + O(x^20)) \\ Colin Barker, Jun 03 2015
(Magma) I:=[99, 10101, 1030199]; [n le 3 select I[n] else 101*Self(n-1) +101*Self(n-2) -Self(n-3): n in [1..40]]; // G. C. Greubel, Feb 16 2023
(SageMath)
A097726=BinaryRecurrenceSequence(102, -1, 1, 103)
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CROSSREFS
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KEYWORD
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nonn,easy,frac
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AUTHOR
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STATUS
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approved
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