Calculating recursive terms of a sequence

Question

I want to calculate resursive terms of a sequence. The following code do this task with fibonacci sequence (sure, could be other sequence).

\documentclass[varwidth,border=5]{standalone}
\usepackage{tikz}
\usepackage{fp}
\usetikzlibrary{fixedpointarithmetic}
\usetikzlibrary{math}

\begin{document}
  \tikzset{fixed point arithmetic}
  \tikzmath{
    function printfib(\i,\f){print {$f_{\i} = \f$\newline};};
    function fibonacci(\n) {
      int \a, \b, \res;
      \a = 0; \b = 1;
      if \n == 0 then { \res = \a; };
      if \n == 1 then { \res = \b; };
      if \n > 1 then {
        for \i in {2,...,\n}{
          \res = \a + \b;
          \a = \b;
          \b = \res;
        };
      };
      return \res;
    };
    int \f, \i;
    for \i in {0,1,...,10}{
      printfib(\i,fibonacci(\i));
    };
  }


\end{document}

However, I would like to print this results into a table, with two columns. The first one are the n values and the second ones the nth term of my sequence. Anyone could help me please to insert instructions to do this? In other words, I provide the value for n and I would like to obtain a table with the n values for my sequence. Thank you very much!

Answer 1

You can use tikzmath to define macros. Such macros, as \fib in the example below, can be used to fill a table. This is a very basic table, you can make it more fancy, and you could use pgfplotstable to fill it.

\documentclass[varwidth,border=5]{standalone}
\usepackage{etoolbox}
\usepackage{tikz}
\usepackage{fp}
\usetikzlibrary{fixedpointarithmetic}
\usetikzlibrary{math}

\begin{document}
  \tikzset{fixed point arithmetic}
  \tikzmath{
    function printfib(\i,\f){print {$f_{\i} = \f$\newline};};
    function fibonacci(\n) {
      int \a, \b, \res;
      \a = 0; \b = 1;
      if \n == 0 then { \res = \a; };
      if \n == 1 then { \res = \b; };
      if \n > 1 then {
        for \i in {2,...,\n}{
          \res = \a + \b;
          \a = \b;
          \b = \res;
        };
      };
      return \res;
    };
    int \f, \i;
    for \i in {0,1,...,10}{
      \fib{\i}=fibonacci(\i);
    };
  }

\def\tmp{$n$ & $f(n)$\\ $0$ & $0$\\}%
\edef\iloop{0}%
\loop
\edef\iloop{\the\numexpr\iloop+1}%
\xappto\tmp{$\iloop$ & $\fib{\iloop}$}%
\gappto\tmp{\\}%
\ifnum\iloop<10\repeat

\begin{tabular}{cc}
\tmp
\end{tabular}

\end{document}