TikZ: How to create a list with calculated entries for a style

Question

I have a TikZ-matrix. And I want to highlight the rows
1, 3, 6, 10, 15, 21, 28,... =n*(n+1)/2

For small examples, I could do it this way:

highlight/.style={  row #1/.style={....}   },
highlight/.list={1,3,6,10,15}

But my question is: Think about a quite bigger number of rows (say 1000) - how can I automate that by using the calculation "n*(n+1)/2"?

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix}
\begin{document}
\begin{tikzpicture}[
highlight/.style={  row #1/.style={nodes={fill=pink}}   },
]
\matrix[matrix of nodes,
highlight/.list={1,3,6,10,15}
](m){
1 \\
2 \\
3 \\
4 \\
5 \\
6 \\
7 \\
8 \\
9 \\
10  \\
11 \\
};
\end{tikzpicture}
\end{document}

Answer 1

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix}

\ExplSyntaxOn
\cs_new:Npn\my_calculate:n #1
  { , \int_eval:n{#1*(#1+1)/2} }

\newcommand\createlist[1]{
  \int_step_function:nnN{1}{#1}\my_calculate:n
}
\ExplSyntaxOff

\begin{document}
\begin{tikzpicture}[
  highlight/.style={row #1/.style={nodes={fill=pink}}},
]
  \matrix[matrix of nodes,
    highlight/.list/.expanded={\createlist{5}}
  ] (m) {
    1 \\
    2 \\
    3 \\
    4 \\
    5 \\
    6 \\
    7 \\
    8 \\
    9 \\
    10 \\
    11 \\
  };
\end{tikzpicture}
\end{document}

Answer 2

Since it's just integer calculations that hopefully don't surpass 2³¹−1 you can use \int_eval:n, \inteval (which is a front-end version of int_eval) or \pgfinteval (which is a clone of the previous) inside the key specification:

highlight/.style={
  row \inteval{#1*(#1+1)/2}/.append style={nodes={fill=pink}}}

If you don't want to alter the highlight key you can use a forwarder, of course:

highlight/.style={row #1/.append style={nodes={fill=pink}}},
highlight'/.style={highlight=\pgfinteval{#1*(#1+1)/2}}

It would also be possible to create something like

highlight/.list wrap={1, ..., 1000}{\inteval{#1*(#1+1)/2}}`

if the previous suggestion are not nice enough.

Code

\documentclass[tikz]{standalone}
\usetikzlibrary{matrix}
\tikzset{
  create column/.style={
    matrix content/.initial=,
    /utils/temp/.style={
      matrix content/.append={##1\pgfmatrixendrow}},
    /utils/temp/.list={#1},
    node contents=\pgfkeysvalueof{/tikz/matrix content}}}
\begin{document}
\tikz[
  highlight/.style={
    row \inteval{#1*(#1+1)/2}/.append style={nodes={fill=pink}}}]
\matrix (m) [
  matrix of nodes,
  highlight/.list={1, ..., 1000},
  create column={1, ..., 1000}];

\tikz[
  highlight/.style={row #1/.append style={nodes={fill=pink}}},
  highlight'/.style={highlight=\pgfinteval{#1*(#1+1)/2}}]
\matrix (m) [
  matrix of nodes,
  highlight'/.list={1, ..., 1000},
  create column={1, ..., 1000}];
\end{document}