OFFSET
0,4
COMMENTS
The limit of A345125(n)/a(n) is Pi.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
Frits Beukers, A rational approach to Pi, Nieuw Archief voor de Wiskunde, December 2000, pp. 372-379.
EXAMPLE
4/(1 + 1^2/(3 + 2^2/5)) = 19/6. So a(3) = 6.
0, 4, 3, 19/6, 160/51, 1744/555, 644/205, 2529/805, 183296/58345, ...
MATHEMATICA
nmax = 25; Join[{1}, Table[4/(1 + ContinuedFractionK[j^2, (2*j + 1), {j, 1, k}]), {k, 0, nmax}] // Denominator] (* Vaclav Kotesovec, Sep 16 2021 *)
PROG
(PARI) a(n) = my(x=0); forstep(i=n, 2, -1, x = (i-1)^2/((2*i-1)+x); ); if (n, denominator(4/(1+x)), denominator(x)); \\ Michel Marcus, Sep 16 2021
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Seiichi Manyama, Sep 16 2021
STATUS
approved