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\usepackage[T1]{fontenc}  % T1 for accents, before babel
\usepackage{amsmath}
\allowdisplaybreaks

\usepackage{needspace}
\usepackage{gensymb}    % for \degree
\usepackage{hyphenat}   % for \hyp hyphenation of words with -

\usepackage[pdfusetitle,
            pdflang={en}, % RFC3066 style ISO639
           ]{hyperref}
\renewcommand\figureautorefname{figure}   % lower case
\usepackage[all]{hypcap} % figure links to top of figure

% breakurl must be after hyperref
% whizzytex circa its version 1.3.3 does something hairy which upsets breakurl,
% so skip when whizzytex previewing
\usepackage{ifthen}
\ifthenelse{\isundefined{\Whizzytex}}{
\usepackage{breakurl} % for breaking long \url in DVI
}

\usepackage{mathtools}  % for \mathclap and showonlyrefs
\mathtoolsset{showonlyrefs=true,showmanualtags=true}

\usepackage{amsthm}

\usepackage{tikz}
\usetikzlibrary{arrows.meta}  % for Latex arrows To[length etc
\usetikzlibrary{bending}      % for arrow [bend]
\usetikzlibrary{calc}         % for ($(...)$) coordinate calculations
\usetikzlibrary{decorations}  % for [decoration=]
\usetikzlibrary{decorations.pathreplacing}  % for decoration=brace
\usetikzlibrary{shapes}       % for shape aspect=1
\tikzset{font=\small,         % same as text
         >=Latex}             % arrowhead style
  % must be capital Latex for [harpoon] half arrows


%------------------------------------------------------------------------------
% personal preferences

\hypersetup{
  pdfborderstyle={/W 0},  % no border on hyperlinks
}

% these must be after \begin{document} to take effect, hence \AtBeginDocument
\AtBeginDocument{%
  \setlength\abovedisplayskip{.7\baselineskip}
  \setlength\belowdisplayskip{.7\baselineskip}
  \setlength\abovedisplayshortskip{.5\baselineskip}
  \setlength\belowdisplayshortskip{.5\baselineskip}
}

% less space after "plain" style \end{theorem} etc
\makeatletter
\g@addto@macro\th@plain{\thm@postskip=1\baselineskip}
\makeatother

%------------------------------------------------------------------------------
% Generic Macros

% GP-DEFINE  default(strictargs,1);

\newcommand\MySlash{\slash\hspace{0pt}}
\newcommand\MyTightDots{.\kern.1em.\kern.1em.}

\newbox\MyNegativePhantomBox
\newcommand\MyNegativePhantom[1]{%
  \setbox\MyNegativePhantomBox\hbox{#1}%
  \hbox to -\wd\MyNegativePhantomBox{}}
% -\wd\MyNegativePhantomBox

% % Uncomment this to see the bounding box around each picture.
% \tikzset{
%   every picture/.append style={
%     execute at end picture={
%       \draw (current bounding box.south west)
%         rectangle (current bounding box.north east);
% }}}


%------------------------------------------------------------------------------
\begin{document}



%------------------------------------------------------------------------------
\clearpage
\section{A045898 Triplets of Hanoi Moves}

Bits of $n$, high to low

\begin{tikzpicture}
    [scale=1.8,
     my box/.style={draw,ellipse,minimum size=1em,inner sep=.15em,outer sep=.2em},
    ]

  \node (1)  at (0,0) [my box] {1};
  \node (2)  at (1.5,0)  [my box] {2};
  \node (3)  at (1.5,-1) [my box] {3};
  \node (4)  at (0,-1) [my box] {4};
  \node (5)  at (.75,-2) [my box] {5};

% GP-DEFINE  expand=[ 1,2; \
% GP-DEFINE           1,3; \
% GP-DEFINE           4,5; \
% GP-DEFINE           1,5; \
% GP-DEFINE           4,3 ];

  \draw [<-,loop left] (1) to node[pos=.5,auto=left] {0} ();
  \draw [->,bend left=10] (1) to node[pos=.5,auto=left] {1} (2);
% GP-Test  expand[1,1] == 1
% GP-Test  expand[1,2] == 2

  \draw [->,bend left=10] (2) to node[pos=.5,auto=left] {0} (1);
  \draw [->] (2) to node[pos=.4,auto=left] {1} (3);
% GP-Test  expand[2,1] == 1
% GP-Test  expand[2,2] == 3

  \draw [->] (3) to node[pos=.5,auto=right] {0} (4);