\documentclass[tikz,border=3mm]{standalone}
\usepackage[svgnames]{xcolor}
\usetikzlibrary{shapes}

\tikzset{triangle path/.style={%
  regular polygon, regular polygon sides=3,
  minimum size=2cm, inner sep=0pt, outer sep=0pt},
triangle draw/.style={%
  draw=gray, regular polygon, regular polygon sides=3,
  minimum size=2cm, inner sep=0pt, outer sep=0pt}
}

\newcommand{\drawgrid}[1]{
\foreach \i [count=\row from 0, remember=\row as \lastrow (initially 0)] in {0,...,#1}{
    \foreach \j [count=\column from 0, remember=\column as \lastcolumn (initially 0)] in {0,...,\i}{
        \ifnum\row=0
            \node[triangle draw](0-0){};
        \else
            \ifnum\column=0
                \node[triangle draw, anchor=north](\row-0) at (\lastrow-0.corner 2) {};
            \else
                \node[triangle draw, anchor=north](\row-\column) at (\lastrow-\lastcolumn.corner 3) {};
            \fi
        \fi}}
}

\newcommand{\viewgrid}[1]{
\foreach \i [count=\row from 0, remember=\row as \lastrow (initially 0)] in {0,...,#1}{
    \foreach \j [count=\column from 0, remember=\column as \lastcolumn (initially 0)] in {0,...,\i}{
        \ifnum\row=0
            \node[triangle path](0-0){0-0};
        \else
            \ifnum\column=0
                \node[triangle path, anchor=north](\row-0) at (\lastrow-0.corner 2) {\row-0};
            \else
                \node[triangle path, anchor=north](\row-\column) at (\lastrow-\lastcolumn.corner 3) {\row-\column};
            \fi
        \fi}}
}

\begin{document}
\begin{tikzpicture}
% draw the triangular grid
\drawgrid{5}
\end{tikzpicture}

\begin{tikzpicture}
% draw the triangular path
\viewgrid{5}
\end{tikzpicture}

\begin{tikzpicture}
% draw the triangular grid
\drawgrid{5}

% draw the little ship
\begin{scope}[draw=black, very thick, fill=CornflowerBlue]
\filldraw[fill opacity=0.5] (5-2.corner 2)--(4-0.corner 1)--(4-1.corner 1)--
         (2-1.corner 1)--(3-2.corner 3)--(4-4.corner 1)--(5-4.corner 2)--cycle;

\draw (4-1.corner 1) -- (4-3.corner 1) (4-2.corner 1)--(2-1.corner 1);
\end{scope}
\end{tikzpicture}

\end{document}