Plotting the sum of a function in TikZ

I am trying to plot a function that is the sum of another function based on the parameter.

A famous example of this is the "sum of squares", however the functions I really want to do this do not have an explicit formula.

The following example shows the result I would like to get and a method how I would like to have it, which is obviously not giving the correct result.

\documentclass[border=10]{standalone}\usepackage{tikz}\usepackage{pgfplots}\pgfplotsset{compat=1.9}\begin{document}  % Explicit formula  \pgfmathdeclarefunction{explicit_sum}{1}{%    \pgfmathparse{(#1*(#1-1))/2}%  }  % The inner function  \pgfmathdeclarefunction{square}{1}{%    \pgfmathparse{#1*#1}%  }  % Compute the sum of another function  % Does not work...  \pgfmathdeclarefunction{manual_sum}{1}{%    %Parameter should be integral    \pgfmathtruncatemacro\cnt{#1}    \pgfmathsetmacro\ret{0}    \foreach \i in {1,...,\cnt} {      \pgfmathsetmacro\ret{\ret + sum(\i)}    }    \pgfmathparse{\ret}  }  \begin{tikzpicture}    \begin{axis}      % Expected      \addplot[samples at={1,...,10}] {explicit_sum(x)};      % Does not work      \addplot[samples at={1,...,10}] {manual_sum(x)};    \end{axis}      \end{tikzpicture}\end{document}