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 A195548 Numerators b(n) of Pythagorean approximations b(n)/a(n) to 1/2. 3

%I #19 Jun 26 2022 02:47:12

%S 0,3,5,8,39,105,136,715,1869,2448,12815,33553,43920,229971,602069,

%T 788120,4126647,10803705,14142232,74049691,193864605,253772064,

%U 1328767775,3478759201,4553754912,23843770275,62423800997,81713816360,427859097159,1120149658761

%N Numerators b(n) of Pythagorean approximations b(n)/a(n) to 1/2.

%C See A195500 for discussion and list of related sequences; see A195547 for Mathematica program.

%F a(n) = (F(n+1)^2-F(n)^2)/(2-((n+2)^2 mod 3)), where F(n)=Fibonacci(n). [_Gary Detlefs_, Oct 15 2011]

%F Empirical G.f.: x*(3+5*x+8*x^2-12*x^3+20*x^4+x^6-x^7)/(1-17*x^3-17*x^6+x^9). [_Colin Barker_, Apr 15 2012]

%Y Cf. A195500, A195547, A195549, A131534.

%K nonn

%O 1,2

%A _Clark Kimberling_, Sep 20 2011

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Last modified September 7 05:42 EDT 2024. Contains 375729 sequences. (Running on oeis4.)