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The On-Line Encyclopedia of Integer Sequences (OEIS)
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 3.2 Final//EN"> <html> <head> <link rel="stylesheet" href="/styles.css"> <meta name="format-detection" content="telephone=no"> <meta http-equiv="content-type" content="text/html; charset=utf-8"> <meta name=viewport content="width=device-width, initial-scale=1"> <meta name="keywords" content="OEIS,integer sequences,Sloane" /> <title>The On-Line Encyclopedia of Integer Sequences (OEIS)</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/history?seq=A051050" function redir() { var host = document.location.hostname; if(host != "oeis.org" && host != "127.0.0.1" && !/^([0-9.]+)$/.test(host) && host != "localhost" && host != "localhost.localdomain") { document.location = "https"+":"+"//"+"oeis"+".org/" + myURL; } } function sf() { if(document.location.pathname == "/" && document.f) document.f.q.focus(); } </script> </head> <body bgcolor=#ffffff onload="redir();sf()"> <div class=loginbar> <div class=login> <a href="/login?redirect=%2fhistory%3fseq%3dA051050">login</a> </div> </div> <div class=center><div class=top> <center> <div class=donors> The OEIS is supported by <a href="http://oeisf.org/#DONATE">the many generous donors to the OEIS Foundation</a>. </div> <div class=banner> <a href="/"><img class=banner border="0" width="600" src="/banner2021.jpg" alt="The On-Line Encyclopedia of Integer Sequences (OEIS)"></a> </div> <div class="motdbox"> <div class="motd"> <p>Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).</p> </div> <div class="donate"> <div id="donate-button-container"> <div id="donate-button"></div> <script src="https://www.paypalobjects.com/donate/sdk/donate-sdk.js" charset="UTF-8"></script> <script> PayPal.Donation.Button({ env:'production', hosted_button_id:'SVPGSDDCJ734A', image: { src:'https://www.paypalobjects.com/en_US/i/btn/btn_donateCC_LG.gif', alt:'Donate with PayPal button', title:'PayPal - The safer, easier way to pay online!', } }).render('#donate-button'); </script> </div> <a href="https://oeisf.org/donate/"> <strong>Other ways to Give</strong> </a> </div> </div> </center> </div></div> <div class=center><div class=pagebody> <div class=searchbarcenter> <form name=f action="/search" method="GET"> <div class=searchbargreet> <div class=searchbar> <div class=searchq> <input class=searchbox maxLength=1024 name=q value="" title="Search Query"> </div> <div class=searchsubmit> <input type=submit value="Search" name=go> </div> <div class=hints> <span class=hints><a href="/hints.html">Hints</a></span> </div> </div> <div class=searchgreet> (Greetings from <a href="/welcome">The On-Line Encyclopedia of Integer Sequences</a>!) </div> </div> </form> </div> <center> <h2 style="margin-top:0; margin-bottom:0;"> Revision History for <a href="/A051050">A051050</a> </h2> (Bold, blue-underlined text is an <ins>addition</ins>; faded, red-underlined text is a <del>deletion</del>.) </center> <br> Showing all changes. <br> <div class=history> <div class=space1></div> <div class=line></div> <div class=seqhead> <div class=seqnumname> <div class=seqnum><a href="/A051050">A051050</a></div> <div class=seqname> Numerator of the probability that the convex hull of n+2 randomly chosen points in the unit ball B^n has n+1 vertices. <br> <font size=-1>(<a href="/history?seq=A051050">history</a>; <a href="/A051050">published version</a>) </font> </div> </div> </div> <div class=resultline></div> <div class="revbar"> <a href="/history/view?seq=A051050&v=8">#8</a> by <a href="/history?user=R.%20J.%20Mathar">R. J. Mathar</a> at Fri Jan 11 15:36:22 EST 2013 </div> <div> <div class=entry> <div class=section> <div class=sectname>STATUS</div> <div class=sectbody> <p class="diffs"><tt><del>editing</del></tt></p> <p class="diffs"><tt><ins>approved</ins></tt></p> </div> </div> </div> </div> <div class=space4></div> <div class=resultline></div> <div class="revbar"> <a href="/history/view?seq=A051050&v=7">#7</a> by <a href="/history?user=R.%20J.%20Mathar">R. J. Mathar</a> at Fri Jan 11 15:36:16 EST 2013 </div> <div> <div class=entry> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <p class="diffs"><tt>Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SylvestersFour-PointProblem.html"><del>Link</del><del> </del><del>to</del><del> </del><del>a</del><del> </del><del>section</del><del> </del><del>of</del><del> </del><del>The</del><del> </del><del>World</del><del> </del><del>of</del><del> </del><del>Mathematics</del><ins>Sylvester</ins><ins>'</ins><ins>s</ins><ins> </ins><ins>Four</ins><ins>-</ins><ins>Point</ins><ins> </ins><ins>Problem</ins>.</a></tt></p> </div> </div> <div class=section> <div class=sectname>STATUS</div> <div class=sectbody> <p class="diffs"><tt><del>approved</del></tt></p> <p class="diffs"><tt><ins>editing</ins></tt></p> </div> </div> </div> </div> <div class=space4></div> <div class=resultline></div> <div class="revbar"> <a href="/history/view?seq=A051050&v=6">#6</a> by <a href="/history?user=Russ%20Cox">Russ Cox</a> at Sat Mar 31 12:38:52 EDT 2012 </div> <div> <div class=entry> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <p class="diffs"><tt><del>Eric Weisstein (eric(AT)weisstein.com)</del></tt></p> <p class="diffs"><tt><ins><a href="/wiki/User:Eric_W._Weisstein">Eric W. Weisstein</a></ins></tt></p> </div> </div> </div> </div> <div class="space4"></div> <div class=discussbar> <div class=discusshead>Discussion</div> <div class=discussnote> <div class=date>Sat Mar 31</div> <div class=time>12:38</div> <pre class=note><span class=user>OEIS Server</span>: https://oeis.org/edit/global/877</pre> </div> </div> <div class=space4></div> <div class=resultline></div> <div class="revbar"> <a href="/history/view?seq=A051050&v=5">#5</a> by <a href="/history?user=N.%20J.%20A.%20Sloane">N. J. A. Sloane</a> at Sun Jun 29 03:00:00 EDT 2008 </div> <div> <div class=entry> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <p class="diffs"><tt><del>E</del><del>.</del><del> </del><del>W</del><del>.</del><del> </del><ins>Eric</ins><ins> </ins>Weisstein<del>,</del><del> </del><ins>'</ins><ins>s</ins><ins> </ins><ins>World</ins><ins> </ins><ins>of</ins><ins> </ins><ins>Mathematics</ins><ins>,</ins><ins> </ins><a href="http://mathworld.wolfram.com/SylvestersFour-PointProblem.html">Link to a section of The World of Mathematics.</a></tt></p> </div> </div> <div class=section> <div class=sectname>KEYWORD</div> <div class=sectbody> <p class="diffs"><tt><span title="a sequence of nonnegative numbers">nonn</span>,<span title="numerators or denominators of sequence of rationals">frac</span><del>,</del><del><span title="added within the last two weeks">new</span></del></tt></p> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <p class="diffs"><tt>Eric <del>W</del><del>.</del><del> </del>Weisstein (eric(AT)weisstein.com)</tt></p> </div> </div> </div> </div> <div class=space4></div> <div class=resultline></div> <div class="revbar"> <a href="/history/view?seq=A051050&v=4">#4</a> by <a href="/history?user=N.%20J.%20A.%20Sloane">N. J. A. Sloane</a> at Fri May 16 03:00:00 EDT 2003 </div> <div> <div class=entry> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <p class="diffs"><tt><ins>E. W. Weisstein, <a href="http://mathworld.wolfram.com/SylvestersFour-PointProblem.html">Link to a section of The World of Mathematics.</a></ins></tt></p> </div> </div> <div class=section> <div class=sectname>KEYWORD</div> <div class=sectbody> <p class="diffs"><tt><span title="a sequence of nonnegative numbers">nonn</span>,<span title="numerators or denominators of sequence of rationals">frac</span><del>,</del><del><span title="added within the last two weeks">new</span></del></tt></p> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <p class="diffs"><tt>Eric W. Weisstein (<del>eww</del><del>@</del><del>wolfram</del><ins>eric</ins><ins>(</ins><ins>AT</ins><ins>)</ins><ins>weisstein</ins>.com)</tt></p> </div> </div> </div> </div> <div class=space4></div> <div class=resultline></div> <div class="revbar"> <a href="/history/view?seq=A051050&v=3">#3</a> by <a href="/history?user=N.%20J.%20A.%20Sloane">N. J. A. Sloane</a> at Sat Jul 22 03:00:00 EDT 2000 </div> <div> <div class=entry> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <p class="diffs"><tt><del><a href="http://mathworld.wolfram.com/SylvestersFour-PointProblem.html">Source</a></del></tt></p> </div> </div> <div class=section> <div class=sectname>KEYWORD</div> <div class=sectbody> <p class="diffs"><tt><span title="a sequence of nonnegative numbers">nonn</span>,<span title="numerators or denominators of sequence of rationals">frac</span><del>,</del><del><span title="added within the last two weeks">new</span></del></tt></p> </div> </div> </div> </div> <div class=space4></div> <div class=resultline></div> <div class="revbar"> <a href="/history/view?seq=A051050&v=2">#2</a> by <a href="/history?user=N.%20J.%20A.%20Sloane">N. J. A. Sloane</a> at Mon May 08 03:00:00 EDT 2000 </div> <div> <div class=entry> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <p class="diffs"><tt><a href="http://<del>www</del><ins>mathworld</ins>.<del>treasure</del><del>-</del><del>troves</del><ins>wolfram</ins>.com/<del>math</del><del>/</del>SylvestersFour-PointProblem.html">Source</a></tt></p> </div> </div> <div class=section> <div class=sectname>KEYWORD</div> <div class=sectbody> <p class="diffs"><tt><span title="a sequence of nonnegative numbers">nonn</span>,<span title="numerators or denominators of sequence of rationals">frac</span><del>,</del><del><span title="added within the last two weeks">new</span></del></tt></p> </div> </div> </div> </div> <div class=space4></div> <div class=resultline></div> <div class="revbar"> <a href="/history/view?seq=A051050&v=1">#1</a> by <a href="/history?user=N.%20J.%20A.%20Sloane">N. J. A. Sloane</a> at Sat Dec 11 03:00:00 EST 1999 </div> <div> <div class=entry> <div class=section> <div class=sectname>NAME</div> <div class=sectbody> <p class="diffs"><tt><ins>Numerator of the probability that the convex hull of n+2 randomly chosen points in the unit ball B^n has n+1 vertices.</ins></tt></p> </div> </div> <div class=section> <div class=sectname>DATA</div> <div class=sectbody> <p class="diffs"><tt><ins>1, 35, 9, 676039, 20000, 322476036831, 45956640625, 109701233401363445369, 3112866107675783424, 95848123849566788297513035239457, 43415602393213717594147325952</ins></tt></p> </div> </div> <div class=section> <div class=sectname>OFFSET</div> <div class=sectbody> <p class="diffs"><tt><ins>0,2</ins></tt></p> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <p class="diffs"><tt><ins><a href="http://www.treasure-troves.com/math/SylvestersFour-PointProblem.html">Source</a></ins></tt></p> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <p class="diffs"><tt><ins>Cf. <a href="/A051051" title="Denominators of the probability that the convex hull of n+2 randomly chosen points in the unit ball B^n has n+1 vertices (wi...">A051051</a>.</ins></tt></p> </div> </div> <div class=section> <div class=sectname>KEYWORD</div> <div class=sectbody> <p class="diffs"><tt><ins><span title="a sequence of nonnegative numbers">nonn</span>,<span title="numerators or denominators of sequence of rationals">frac</span></ins></tt></p> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <p class="diffs"><tt><ins>Eric W. Weisstein (eww@wolfram.com)</ins></tt></p> </div> </div> <div class=section> <div class=sectname>STATUS</div> <div class=sectbody> <p class="diffs"><tt><ins>approved</ins></tt></p> </div> </div> </div> </div> <div class=space4></div> <div class=space10></div> </div> </div></div> <p> <div class=footerpad></div> <div class=footer> <center> <div class=bottom> <div class=linksbar> <a href="/">Lookup</a> <a href="/wiki/Welcome"><font color="red">Welcome</font></a> <a href="/wiki/Main_Page"><font color="red">Wiki</font></a> <a href="/wiki/Special:RequestAccount">Register</a> <a href="/play.html">Music</a> <a href="/plot2.html">Plot 2</a> <a href="/demo1.html">Demos</a> <a href="/wiki/Index_to_OEIS">Index</a> <a href="/webcam">WebCam</a> <a href="/Submit.html">Contribute</a> <a href="/eishelp2.html">Format</a> <a href="/wiki/Style_Sheet">Style Sheet</a> <a href="/transforms.html">Transforms</a> <a href="/ol.html">Superseeker</a> <a href="/recent">Recents</a> </div> <div class=linksbar> <a href="/community.html">The OEIS Community</a> </div> <div class=linksbar> Maintained by <a href="http://oeisf.org">The OEIS Foundation Inc.</a> </div> <div class=dbinfo>Last modified December 3 16:59 EST 2024. 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