Draw dotted line with circled dots and automatic spacing

I'm trying to create dotted lines with tikz where every dot has a defined size and a circle around it, with also a defined size.

First I applied this answer to create a dash pattern:

\tikzset{    dot diameter/.store in=\dot@diameter,    dot diameter=3pt,    dot spacing/.store in=\dot@spacing,    dot spacing=10pt,    dots/.style={        line width=\dot@diameter,        line cap=round,        dash pattern=on 0pt off \dot@spacing    }}

Then I plot these dotted lines in black - white - black on top of each other to achieve the desired effect. How can I change the tikzset to get this in one step?

The next problem is that it requires a defined dot-spacing which is fine if I'd knew the distance between the endpoints of my line, which I usually don't, so I'm fiddling around with the spacing manually. But I'd like to have a circled dot at the beginning and end node and the rest of the dots equally spaced inbetween. How can I achieve that equal distribution? Is it possible to define, say, exactly 11 dots on that line, equally distributed?

Thank you!

MWE

\documentclass{article}\usepackage{tikz}\makeatletter\tikzset{    dot diameter/.store in=\dot@diameter,    dot diameter=3pt,    dot spacing/.store in=\dot@spacing,    dot spacing=10pt,    dots/.style={        line width=\dot@diameter,        line cap=round,        dash pattern=on 0pt off \dot@spacing    }}\makeatother\begin{document}    \begin{tikzpicture}    \coordinate (A1) at (1,1);    \coordinate (B1) at (5,1);    \coordinate (A2) at (1,1.5);    \coordinate (B2) at (5,1.5);    % for reference frame    \draw [black, thick]   (A1.center) -- (B1.center) -- (B2.center) -- (A2.center) -- (A1.center);    % three dot layers #1    \draw [black, dot diameter=3mm, dot spacing=3.8mm, dots]   (A1.center) -- (B1.center);    \draw [white, dot diameter=2.5mm, dot spacing=3.8mm, dots]  (A1.center) -- (B1.center);    \draw [black, dot diameter=1mm, dot spacing=3.8mm, dots]    (A1.center) -- (B1.center);    % three dot layers #2    \draw [black, dot diameter=3mm, dot spacing=4mm, dots]   (A2.center) -- (B2.center);    \draw [white, dot diameter=2.5mm, dot spacing=4mm, dots]  (A2.center) -- (B2.center);    \draw [black, dot diameter=1mm, dot spacing=4mm, dots]    (A2.center) -- (B2.center);    \end{tikzpicture}\end{document}

The solid line is just for orientation, there shouldn't be a connect between the dots. The upper dotted line is manually adjusted to get the correct spacing.