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Fibonacci like sequence $f(n) = f(n-1) + f(n-2) + f(n/2)$ and closed form limits?
Consider
$$f(1) = g(1) = 1$$
$$f(2) = A,g(2) = B$$
$$f(3) = 1 + A,g(3) = 1+B$$
And for $n>3$ :
$$f(n) = f(n-1) + f(n-2) + f(n/2)$$
$$g(n) = g(n-1) + g(n-2)$$
where we take the integer part of the ...
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2 conjectured recursion limits for $e$ and $\pi$. [duplicate]
Consider the following recursions
$$ x_{n+2} = x_{n+1} + \frac{x_n}{n} $$
$$y_{n+2} = \frac{ y_{n+1}}{n} + y_n $$
I have been toying around with different starting values ( complex Numbers ) , ...
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