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\begin{document}

\section{Addendum}

These results - computed since publication - are additional to those reported in Appendix A above.

\bigskip

$\mathbf{h=2}$

\smallskip

\begin{tabular}{r@{\hspace{.15in}}r@{\hspace{.15in}}rrrrrrrrrrrrrrrrrrrrrr}
$k$&amp;\multicolumn{1}{c}{$n(2,k)$}&amp;&amp;$a_i$\\
23 &amp; 196 &amp;&amp; 1&amp;3&amp;4&amp;6&amp;10&amp;13&amp;15&amp;21&amp;29&amp;37&amp;45&amp;53\\
 &amp; &amp;&amp; &amp; &amp; &amp;61&amp;69&amp;77&amp;85&amp;89&amp;91&amp;94&amp;95&amp;98&amp;100&amp;104\\
23 &amp; 196 &amp;&amp; 1&amp;3&amp;4&amp;6&amp;10&amp;13&amp;15&amp;21&amp;29&amp;37&amp;45&amp;53\\
 &amp; &amp;&amp; &amp; &amp; &amp;61&amp;69&amp;77&amp;85&amp;89&amp;91&amp;94&amp;95&amp;96&amp;98&amp;100\\
23 &amp; 196 &amp;&amp; 1&amp;3&amp;4&amp;6&amp;10&amp;13&amp;15&amp;21&amp;29&amp;37&amp;45&amp;53\\
 &amp; &amp;&amp; &amp; &amp; &amp;61&amp;69&amp;77&amp;83&amp;85&amp;88&amp;92&amp;94&amp;95&amp;97&amp;98\\
\end{tabular}

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$\mathbf{h=3}$

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\begin{tabular}{r@{\hspace{.15in}}r@{\hspace{.15in}}rrrrrrrrrrrrrrrr}
$k$&amp;\multicolumn{1}{c}{$n(3,k)$}&amp;&amp;$a_i$\\
15 &amp; 385 &amp;&amp; 1&amp;3&amp;8&amp;12&amp;19&amp;25&amp;34&amp;36&amp;57&amp;98&amp;118&amp;128&amp;168&amp;178&amp;198\\
15 &amp; 385 &amp;&amp; 1&amp;4&amp;5&amp;16&amp;18&amp;29&amp;37&amp;43&amp;52&amp;78&amp;98&amp;148&amp;158&amp;178&amp;188\\
\end{tabular}

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$\mathbf{h=4}$

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\begin{tabular}{r@{\hspace{.15in}}r@{\hspace{.15in}}rrrrrrrrrrrrr}
$k$&amp;\multicolumn{1}{c}{$n(4,k)$}&amp;&amp;$a_i$\\
12 &amp; 700 &amp;&amp;  1&amp;5&amp;8&amp;20&amp;22&amp;29&amp;45&amp;106&amp;174&amp;240&amp;311&amp;321\\
\end{tabular}

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\pagebreak

$\mathbf{k=4}$

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For $55 \leq h \leq 302$, $n(h,4)$ and $a_i$ are given by one of the following three sets of formulae:

\bigskip

$\begin{array}{rrcl}
        (A): &amp; a_2 &amp; = &amp; (9t + c_{21})\\
        &amp; a_3 &amp; = &amp; (4t + c_{31}) + (3t + c_{32})a_2\\
        &amp; a_4 &amp; = &amp; (7t + c_{41}) + (2t + c_{42})a_2 + (2t + c_{43})a_3\\
        &amp; n(h,4) &amp; = &amp; (2t + c_{51}) + ( t + c_{52})a_2 + (6t + c_{53})a_3 + (3t + c_{54})a_4
\end{array}$

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$\begin{array}{rrcl}
        (B): &amp; a_2 &amp; = &amp; (9t + c_{21})\\
        &amp; a_3 &amp; = &amp; (2t + c_{31}) + (3t + c_{32})a_2\\
        &amp; a_4 &amp; = &amp; (7t + c_{41}) + (2t + c_{42})a_2 + (2t + c_{43})a_3\\
        &amp; n(h,4) &amp; = &amp; (4t + c_{51}) + (3t + c_{52})a_2 + (2t + c_{53})a_3 + (3t + c_{54})a_4
\end{array}$

\bigskip

$\begin{array}{rrcl}
        (C): &amp; a_2 &amp; = &amp; (9t + c_{21})\\
        &amp; a_3 &amp; = &amp; (4t + c_{31}) + (3t + c_{32})a_2\\
        &amp; a_4 &amp; = &amp; (7t + c_{41}) + (2t + c_{42})a_2 + (2t + c_{43})a_3\\
        &amp; n(h,4) &amp; = &amp; (t + c_{51}) + (4t + c_{52})a_2 + (6t + c_{53})a_3 + (3t + c_{54})a_4
\end{array}$

\bigskip

where  $h = 12t + r$,  $0 \leq r \leq 11$,  and $c_{ij}$ are given in the following table:


\vspace{-.1in}
\begin{center}
\begin{tabular}{rrrrrrrrrrrrrr}
$r$&amp;&amp;&amp;$c_{21}$&amp;$c_{31}$&amp;$c_{32}$&amp;$c_{41}$&amp;$c_{42}$&amp;$c_{43}$&amp;$c_{51}$&amp;$c_{52}$&amp;$c_{53}$&amp;$c_{54}$&amp;Valid for:\\
0&amp;A&amp;&amp;2&amp;1&amp;0&amp;1&amp;0&amp;1&amp;$-3$&amp;0&amp;4&amp;$-1$&amp;$ 4 \leq t \leq  5$\\
0&amp;A&amp;&amp;1&amp;0&amp;0&amp;0&amp;0&amp;0&amp;$-2$&amp;0&amp;1&amp;1&amp;$ 6 \leq t \leq 11$\\
0&amp;B&amp;&amp;2&amp;2&amp;$-1$&amp;3&amp;$-1$&amp;0&amp;$-1$&amp;$-2$&amp;$-1$&amp;4&amp;$12 \leq t \leq 25$\\
1&amp;A&amp;&amp;1&amp;0&amp;2&amp;1&amp;1&amp;0&amp;0&amp;0&amp;1&amp;0&amp;$ 5 \leq t \leq 25$\\
2&amp;A&amp;&amp;2&amp;1&amp;1&amp;1&amp;1&amp;1&amp;$-3$&amp;1&amp;4&amp;0&amp;$ 5 \leq t \leq  6$\\
2&amp;A&amp;&amp;1&amp;0&amp;2&amp;1&amp;1&amp;0&amp;0&amp;0&amp;1&amp;1&amp;$ 7 \leq t \leq 20$\\
2&amp;B&amp;&amp;5&amp;3&amp;$-1$&amp;6&amp;$-1$&amp;0&amp;0&amp;$-2$&amp;$-1$&amp;5&amp;$21\leq t\leq25$\\
3&amp;A&amp;&amp;3&amp;1&amp;2&amp;2&amp;1&amp;1&amp;$-1$&amp;0&amp;4&amp;0&amp;$ 1 \leq t \leq 24$\\
4&amp;A&amp;&amp;3&amp;1&amp;2&amp;2&amp;1&amp;1&amp;$-1$&amp;0&amp;4&amp;1&amp;$ 2 \leq t \leq 24$\\
5&amp;A&amp;&amp;3&amp;1&amp;2&amp;2&amp;1&amp;1&amp;$-1$&amp;0&amp;4&amp;2&amp;$ 4 \leq t \leq 24$\\
6&amp;A&amp;&amp;3&amp;1&amp;2&amp;2&amp;1&amp;1&amp;$-1$&amp;0&amp;4&amp;3&amp;$ 5 \leq t \leq 24$\\
7&amp;A&amp;&amp;7&amp;3&amp;2&amp;5&amp;1&amp;2&amp;$-1$&amp;0&amp;7&amp;1&amp;$ 2 \leq t \leq 11$\\
7&amp;A&amp;&amp;8&amp;4&amp;1&amp;7&amp;1&amp;0&amp;0&amp;1&amp;1&amp;5&amp;$12 \leq t \leq 24$\\
8&amp;A&amp;&amp;7&amp;3&amp;3&amp;5&amp;2&amp;2&amp;$-1$&amp;1&amp;7&amp;1&amp;$1 \leq t \leq 16$\\
8&amp;A&amp;&amp;8&amp;4&amp;1&amp;7&amp;1&amp;0&amp;0&amp;1&amp;1&amp;6&amp;$	17 \leq t \leq 24$\\
9&amp;A&amp;&amp;7&amp;3&amp;3&amp;5&amp;2&amp;2&amp;$-1$&amp;1&amp;7&amp;2&amp;$	1 \leq t \leq 21$\\
9&amp;A&amp;&amp;8&amp;4&amp;1&amp;7&amp;1&amp;0&amp;0&amp;1&amp;1&amp;7&amp;$22 \leq t \leq 24$\\
10&amp;A&amp;&amp;7&amp;3&amp;3&amp;5&amp;2&amp;2&amp;$-1$&amp;1&amp;7&amp;3&amp;$	4 \leq t \leq 19$\\
10&amp;C&amp;&amp;11&amp;6&amp;1&amp;10&amp;1&amp;0&amp;0&amp;3&amp;0&amp;7&amp;$ 20\leq t\leq24$\\   
11&amp;A&amp;&amp;10&amp;4&amp;3&amp;7&amp;2&amp;2&amp;0&amp;1&amp;7&amp;3&amp;$	2 \leq t \leq  7$\\
11&amp;B&amp;&amp;11&amp;4&amp;2&amp;10&amp;1&amp;2&amp;3&amp;1&amp;1&amp;6&amp;$ 8 \leq t \leq 22$\\
11&amp;A&amp;&amp;11&amp;5&amp;2&amp;9&amp;2&amp;0&amp;1&amp;2&amp;1&amp;7&amp;$t = 23$\\
11&amp;B&amp;&amp;12&amp;5&amp;1&amp;12&amp;1&amp;0&amp;3&amp;0&amp;-1&amp;10&amp;$  24 \leq t \leq 24$\\
\end{tabular}
\end{center}

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$\mathbf{k=5}$

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\begin{tabular}{r@{\hspace{.2in}}r@{\hspace{.2in}}rrrrrr}
$h$&amp;\multicolumn{1}{c}{$n(h,5)$} &amp;&amp; $a_1$&amp;$a_2$&amp;$a_3$&amp;$a_4$&amp;$a_5$\\
68 &amp; 2330896 &amp;&amp; 1&amp;47&amp;1000&amp;16255&amp;123331\\
69 &amp; 2496702 &amp;&amp; 1&amp;53&amp;752&amp;16196&amp;139500\\
70 &amp; 2653201 &amp;&amp; 1&amp;52&amp;789&amp;15540&amp;133254\\
71 &amp; 2846834 &amp;&amp; 1&amp;53&amp;804&amp;16640&amp;143028\\
72 &amp; 3047485 &amp;&amp; 1&amp;57&amp;866&amp;17811&amp;153105\\
73 &amp; 3250580 &amp;&amp; 1&amp;55&amp;910&amp;17943&amp;171807\\
74 &amp; 3429203 &amp;&amp; 1&amp;58&amp;960&amp;18929&amp;181248\\
75 &amp; 3629795 &amp;&amp; 1&amp;59&amp;1013&amp;18977&amp;182285\\
76 &amp; 3864527 &amp;&amp; 1&amp;63&amp;980&amp;20223&amp;194059\\
77 &amp; 4103963 &amp;&amp; 1&amp;56&amp;906&amp;20468&amp;196209\\
78 &amp; 4416370 &amp;&amp; 1&amp;59&amp;1013&amp;21001&amp;201513\\
79 &amp; 4643287 &amp;&amp; 1&amp;62&amp;1065&amp;22080&amp;211867\\
80 &amp; 4975426 &amp;&amp; 1&amp;65&amp;1141&amp;23658&amp;227046\\
81 &amp; 5223883 &amp;&amp; 1&amp;63&amp;1145&amp;23756&amp;227980\\
82 &amp; 5519971 &amp;&amp; 1&amp;66&amp;1200&amp;24898&amp;263837\\
83 &amp; 5796515 &amp;&amp; 1&amp;62&amp;1150&amp;25011&amp;264322\\
84 &amp; 6139689 &amp;&amp; 1&amp;60&amp;1090&amp;26793&amp;256691\\
85 &amp; 6513282 &amp;&amp; 1&amp;60&amp;1090&amp;26853&amp;284084\\
86 &amp; 6912409 &amp;&amp; 1&amp;69&amp;1255&amp;28480&amp;301525\\
87 &amp; 7258582 &amp;&amp; 1&amp;63&amp;1168&amp;29884&amp;316651\\
88 &amp; 7677138 &amp;&amp; 1&amp;72&amp;1336&amp;31584&amp;334950\\
89 &amp; 8029729 &amp;&amp; 1&amp;67&amp;1285&amp;31617&amp;366107\\
90 &amp; 8525267 &amp;&amp; 1&amp;70&amp;1412&amp;32085&amp;371775\\
\end{tabular}

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$\mathbf{k=6}$

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\begin{tabular}{r@{\hspace{.2in}}r@{\hspace{.2in}}rrrrrrr}
$h$&amp;\multicolumn{1}{c}{$n(h,6)$}&amp;&amp;$a_1$&amp;$a_2$&amp;$a_3$&amp;$a_4$&amp;$a_5$&amp;$a_6$\\
26 &amp; 156744 &amp;&amp; 1&amp;19&amp;177&amp;816&amp;6708&amp;18060\\
\end{tabular}

\bigskip

$\mathbf{k=7}$

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\begin{tabular}{r@{\hspace{.2in}}r@{\hspace{.2in}}rrrrrrrr}
$h$&amp;\multicolumn{1}{c}{$n(h,7)$}&amp;&amp;$a_1$&amp;$a_2$&amp;$a_3$&amp;$a_4$&amp;$a_5$&amp;$a_6$&amp;$a_7$\\
14 &amp; 24466 &amp;&amp; 1&amp;12&amp;52&amp;225&amp;546&amp;3033&amp;5464\\
\end{tabular}

\pagebreak


\end{document}
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