02 Jan '18 16:261 edit

What is the formula for this infinite sequence of integers?

3, 5, 11, 29, 85, 265, 859, 2861, 9725, 33593, 117573, ...?

This was generated via Monte Carlo Method (MCM) over many hours of computer program run time using a program I made especially for this and only this.

I then spent two whole days trying in vain to find the formula for it and now given up trying but hope someone here smarter than me might be able to find it.

I tried wolframAlpha it but for some reason wolframAlpha gives me only complete gibberish with this input.

The MCM outputs a floating-point real number estimate representing the integer and that real number is then rounded off to the nearest odd-number integer (notice that all of these numbers are odd numbers) and that estimate becomes less and less reliable as the input value increases so I have only shown the first 11 output values because I only consider only the first 11 to be sufficiently reliable.

I have reason to think that factorials may be in the required formula.

3, 5, 11, 29, 85, 265, 859, 2861, 9725, 33593, 117573, ...?

This was generated via Monte Carlo Method (MCM) over many hours of computer program run time using a program I made especially for this and only this.

I then spent two whole days trying in vain to find the formula for it and now given up trying but hope someone here smarter than me might be able to find it.

I tried wolframAlpha it but for some reason wolframAlpha gives me only complete gibberish with this input.

The MCM outputs a floating-point real number estimate representing the integer and that real number is then rounded off to the nearest odd-number integer (notice that all of these numbers are odd numbers) and that estimate becomes less and less reliable as the input value increases so I have only shown the first 11 output values because I only consider only the first 11 to be sufficiently reliable.

I have reason to think that factorials may be in the required formula.