# 0 above the Pascal-triangle?

The Pascal triangle for binomial coefficients starts with 1 in line 1 and goes on with 1 1 in line 2, 1 2 1 in line 3, and so on.

Pascal's triangle in tikz

show how one may write up solutions in tikz.

Here is the adapted version which I prefer:

\begin{tikzpicture}[rotate=-90]
\foreach \x in {0,1,...,3}
{
\foreach \y in {0,...,\x}
{
\pgfmathsetmacro\binom{factorial(\x)/(factorial(\y)*factorial(\x-\y))}
\pgfmathsetmacro\shift{\x/2}
\node[xshift=-\shift cm] at (\x,\y) {\pgfmathprintnumber\binom};
}
}
\end{tikzpicture}


How do I write up a variant which has 0 in the first line, 1 in the second line, 1 1 in the third line and thereafter goes on as the usual Pascal's triangle?

\node at (-1,0) {0}; \documentclass[border=5mm]{standalone}
\usepackage{tikz}
\begin{document}

\begin{tikzpicture}[rotate=-90]
\node at (-1,0) {0};
\foreach \x in {0,1,...,3}
{
\foreach \y in {0,...,\x}
{
\pgfmathsetmacro\binom{factorial(\x)/(factorial(\y)*factorial(\x-\y))}
\pgfmathsetmacro\shift{\x/2}
\node[xshift=-\shift cm] at (\x,\y) {\pgfmathprintnumber\binom};
}
}
\end{tikzpicture}

\end{document}



Just a small alternative to @Torbjorn's answer (a trick he taught me here ) to avoid using (annoying IMHO, \pgfmathsetmacro), include the variables to evaluate directly in the loop.

More details in pfg manual v3.1.5.b p1003, section 89 Repeating Things: The Foreach Statement. \documentclass[border=5mm]{standalone}
\usepackage{tikz}
\begin{document}

\begin{tikzpicture}[rotate=-90]
\node at (-1,0) {0};
\foreach \x in {0,1,...,3}
{
\foreach [evaluate ={
\binom = factorial(\x)/(factorial(\y)*factorial(\x-\y));
\shift = \x/2 ;
}] \y in {0,...,\x}
{\node[xshift=-\shift cm] at (\x,\y) {\pgfmathprintnumber\binom};}
}
\end{tikzpicture}

\end{document}

• +1 Where is documented evaluate ={...} as you used it in the manual? – AndréC Aug 2 '20 at 6:09
• @AndréC PGF manual 3.1.5.b p. 1003. section 89 Repeating Things: The Foreach Statement – JeT Aug 2 '20 at 19:54
• The problem is that it looks more like the syntax of the math library on page 704 since it says evaluate={...}. But you haven't loaded this library. And yet with the syntax of this library it works. The syntax of the foreach is not the same as the one you wrote. Maybe it's a syntax initiated on an old version of tikz? – AndréC Aug 2 '20 at 19:58
• @AndréC Etrange ! Trying a \pgfversion, it tells me tikz.sty 2020/01/08 v3.1.5b (3.1.5b) pgf.sty 2020/01/08 v3.1.5b (3.1.5b) which does not seem too old. – JeT Aug 2 '20 at 20:03
• No, it's not strange, there's a lot of code in the latest manual that comes from old manuals and is not documented. And since the code you used is not documented in this manual I wonder which manual it is documented in. It's classic look here: What do “-to” and “pre=moveto” do in TikZ arrows? – AndréC Aug 2 '20 at 20:10