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

0, 3, 5, 8, 39, 105, 136, 715, 1869, 2448, 12815, 33553, 43920, 229971, 602069, 788120, 4126647, 10803705, 14142232, 74049691, 193864605, 253772064, 1328767775, 3478759201, 4553754912, 23843770275, 62423800997, 81713816360, 427859097159, 1120149658761

Offset: 1

Author

Clark Kimberling, Sep 20 2011

Keywords

• nonn

Comments

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

Crossrefs

Cf. A195500, A195547, A195549, A131534.

Formula

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]

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]