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 A195616 Denominators a(n) of Pythagorean approximations b(n)/a(n) to 3. 5
 12, 444, 16872, 640680, 24328980, 923860548, 35082371856, 1332206269968, 50588755886940, 1921040517433740, 72948950906595192, 2770139093933183544, 105192336618554379492, 3994538652411133237140, 151687276455004508631840 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See A195500 for a discussion and references. LINKS Colin Barker, Table of n, a(n) for n = 1..633 Index entries for linear recurrences with constant coefficients, signature (37,37,-1). FORMULA a(n) = 37*a(n-1)+37*a(n-2)-a(n-3). - Colin Barker, Jun 04 2015 G.f.: 12*x / ((x+1)*(x^2-38*x+1)). - Colin Barker, Jun 04 2015 MATHEMATICA r = 3; z = 20; p[{f_, n_}] := (#1[[2]]/#1[[       1]] &)[({2 #1[[1]] #1[[2]], #1[[1]]^2 - #1[[          2]]^2} &)[({Numerator[#1], Denominator[#1]} &)[      Array[FromContinuedFraction[         ContinuedFraction[(#1 + Sqrt[1 + #1^2] &)[f], #1]] &, {n}]]]]; {a, b} = ({Denominator[#1], Numerator[#1]} &)[   p[{r, z}]]  (* A195616, A195617 *) Sqrt[a^2 + b^2] (* A097315 *) (* Peter J. C. Moses, Sep 02 2011 *) PROG (PARI) Vec(12*x/((x+1)*(x^2-38*x+1)) + O(x^20)) \\ Colin Barker, Jun 04 2015 CROSSREFS Cf. A195500, A195617, A097315. Sequence in context: A246502 A281248 A338960 * A126603 A291996 A192601 Adjacent sequences:  A195613 A195614 A195615 * A195617 A195618 A195619 KEYWORD nonn,easy,frac AUTHOR Clark Kimberling, Sep 22 2011 STATUS approved

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Last modified August 14 05:20 EDT 2022. Contains 356110 sequences. (Running on oeis4.)