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[SPAM] [obm-l] Combinatória

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Queria um reality check dos participantes sobre esta quest&atilde;o:<br>
<br>
S&atilde;o dados <i>n</i> pontos em um plano e unem-se estes pontos dois a
dois formando retas, de tal forma que:<br>
<ol>
  <li>Nunca tr&ecirc;s pontos quaisquer pertencem &agrave; mesma reta;</li>
  <li>Nunca duas retas quaisquer s&atilde;o paralelas;</li>
  <li>Nunca tr&ecirc;s retas quaisquer interceptam-se no mesmo ponto.</li>
</ol>
Determinar o n&uacute;mero <i>N</i> dos pontos de interse&ccedil;&atilde;o destas retas que
sejam distintos dos <i>n</i> pontos dados.<br>
<br>
A resposta que encontrei foi: <i>N</i>=0 se <i>n</i>&lt;4; <i>N</i>=somat&oacute;rio
para <i>k</i>=4 at&eacute; <i>n</i> de [((<i>k</i>^3+11<i>k</i>)/2)-3(<i>k</i>^2+1)]&nbsp;
se <i>n</i>&gt;=4.<br>
<br>
[ ]'s<br>
<br>
<font color="#6666cc"><big><b>J. R. Smolka</b></big></font> <br>
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