A195568 - OEIS

%I #12 Jun 05 2015 03:19:38

%S 3,8,120,637,2176,30848,164483,561288,7958776,42435837,144810240,

%T 2053333248,10948281603,37360480520,529752019320,2824614217597,

%U 9638859164032,136673967651200,728739519858563,2486788303839624,35261353901990392

%N Denominators a(n) of Pythagorean approximations b(n)/a(n) to 7/4.

%C See A195500 for a discussion and references.

%F Empirical g.f.: x*(3*x^6+8*x^5+120*x^4-134*x^3+120*x^2+8*x+3) / (x^9-257*x^6-257*x^3+1). - _Colin Barker_, Jun 04 2015

%t r = 7/4; z = 26;

%t p[{f_, n_}] := (#1[[2]]/#1[[

%t       1]] &)[({2 #1[[1]] #1[[2]], #1[[1]]^2 - #1[[

%t          2]]^2} &)[({Numerator[#1], Denominator[#1]} &)[

%t      Array[FromContinuedFraction[

%t         ContinuedFraction[(#1 + Sqrt[1 + #1^2] &)[f], #1]] &, {n}]]]];

%t {a, b} = ({Denominator[#1], Numerator[#1]} &)[

%t   p[{r, z}]]  (* A195568, A195569 *)

%t Sqrt[a^2 + b^2] (* A195570 *)

%t (* _Peter J. C. Moses_, Sep 02 2011 *)

%Y Cf. A195500, A195569, A195570.

%K nonn

%O 1,1

%A _Clark Kimberling_, Sep 21 2011