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A195615 Numerators b(n) of Pythagorean approximations b(n)/a(n) to 2. 3

%I

%S 15,273,4895,87841,1576239,28284465,507544127,9107509825,163427632719,

%T 2932589879121,52623190191455,944284833567073,16944503814015855,

%U 304056783818718321,5456077604922913919,97905340104793732225,1756840044281364266127

%N Numerators b(n) of Pythagorean approximations b(n)/a(n) to 2.

%C See A195500 for discussion and list of related sequences; see A195614 for Mathematica program.

%H Colin Barker, <a href="/A195615/b195615.txt">Table of n, a(n) for n = 1..797</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (17,17,-1).

%F a(n) = 17*a(n-1)+17*a(n-2)-a(n-3). G.f.: -x*(x^2-18*x-15) / ((x+1)*(x^2-18*x+1)). - _Colin Barker_, Jun 04 2015

%F a(n) = ((-1)^n-(-2+sqrt(5))*(9+4*sqrt(5))^(-n)+(2+sqrt(5))*(9+4*sqrt(5))^n)/5. - _Colin Barker_, Mar 04 2016

%o (PARI) Vec(-x*(x^2-18*x-15)/((x+1)*(x^2-18*x+1)) + O(x^50)) \\ _Colin Barker_, Jun 04 2015

%Y Cf. A195500, A195614, A007805.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Sep 22 2011

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Last modified August 8 16:09 EDT 2022. Contains 356015 sequences. (Running on oeis4.)