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A195548 Numerators b(n) of Pythagorean approximations b(n)/a(n) to 1/2. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..30.

FORMULA

a(n) = (F(n+1)^2-F(n)^2)/(2-((n+2)^2 mod 3)), where F(n)=Fibonacci(n). [From 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]

CROSSREFS

Cf. A195500, A195547, A195549, A131534.

Sequence in context: A108460 A249951 A027520 * A174529 A174442 A109342

Adjacent sequences:  A195545 A195546 A195547 * A195549 A195550 A195551

KEYWORD

nonn

AUTHOR

Clark Kimberling, Sep 20 2011

STATUS

approved

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Last modified October 28 16:41 EDT 2021. Contains 348329 sequences. (Running on oeis4.)