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A244242 - 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>A244242 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A244242" 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=%2fA244242">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="A244242 - OEIS"></a> </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> <div class=sequence> <div class=space1></div> <div class=line></div> <div class=seqhead> <div class=seqnumname> <div class=seqnum> A244242 </div> <div class=seqname> Number of partitions of n into 6 parts such that every i-th smallest part (counted with multiplicity) is different from i. </div> </div> <div class=scorerefs> 2 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>1, 6, 16, 31, 52, 76, 107, 143, 184, 233, 289, 354, 427, 512, 606, 716, 835, 972, 1122, 1292, 1476, 1685, 1909, 2161, 2432, 2734, 3057, 3417, 3799, 4222, 4673, 5168, 5693, 6270, 6879, 7545, 8249, 9014, 9821, 10698, 11619, 12616, 13665, 14795, 15981, 17259</div> <div class=seqdatalinks> (<a href="/A244242/list">list</a>; <a href="/A244242/graph">graph</a>; <a href="/search?q=A244242+-id:A244242">refs</a>; <a href="/A244242/listen">listen</a>; <a href="/history?seq=A244242">history</a>; <a href="/search?q=id:A244242&fmt=text">text</a>; <a href="/A244242/internal">internal format</a>) </div> </div> </div> <div class=entry> <div class=section> <div class=sectname>OFFSET</div> <div class=sectbody> <div class=sectline>27,2</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline>Alois P. Heinz, <a href="/A244242/b244242.txt">Table of n, a(n) for n = 27..1000</a></div> </div> </div> <div class=section> <div class=sectname>FORMULA</div> <div class=sectbody> <div class=sectline>Conjectures from <a href="/wiki/User:Chai_Wah_Wu">Chai Wah Wu</a>, Apr 18 2024: (Start)</div> <div class=sectline>a(n) = a(n-1) + a(n-2) - a(n-5) - 2*a(n-7) + a(n-9) + a(n-10) + a(n-11) + a(n-12) - 2*a(n-14) - a(n-16) + a(n-19) + a(n-20) - a(n-21) for n > 57.</div> <div class=sectline>G.f.: x^27*(-x^30 + 2*x^25 + 2*x^24 + 2*x^23 + 4*x^22 + 2*x^21 + x^20 - 9*x^19 - 12*x^18 - 16*x^17 - 12*x^16 + x^15 + 13*x^14 + 24*x^13 + 25*x^12 + 20*x^11 + 3*x^10 - 11*x^9 - 23*x^8 - 22*x^7 - 15*x^6 - 6*x^5 + 5*x^4 + 9*x^3 + 9*x^2 + 5*x + 1)/((x - 1)^6*(x + 1)^3*(x^2 + 1)*(x^2 - x + 1)*(x^2 + x + 1)^2*(x^4 + x^3 + x^2 + x + 1)). (End)</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Column k=6 of <a href="/A238406" title="Number T(n,k) of partitions of n into k parts such that every i-th smallest part (counted with multiplicity) is different fr...">A238406</a>.</div> <div class=sectline>Sequence in context: <a href="/A115007" title="Row 3 of array in A114999.">A115007</a> <a href="/A005891" title="Centered pentagonal numbers: (5n^2+5n+2)/2; crystal ball sequence for 3.3.3.4.4. planar net.">A005891</a> <a href="/A108182" title="Cumulative sum of antisquares (A080255).">A108182</a> * <a href="/A092286" title="Fourth diagonal (m=3) of triangle A084938; a(n) = A084938(n+3,n) = (n^3 + 9*n^2 + 26*n)/6.">A092286</a> <a href="/A301723" title="Partial sums of A301722.">A301723</a> <a href="/A288113" title="Number of Dyck paths of semilength n such that each level has exactly six peaks or no peaks.">A288113</a></div> <div class=sectline>Adjacent sequences: <a href="/A244239" title="Number of partitions of n into 3 parts such that every i-th smallest part (counted with multiplicity) is different from i.">A244239</a> <a href="/A244240" title="Number of partitions of n into 4 parts such that every i-th smallest part (counted with multiplicity) is different from i.">A244240</a> <a href="/A244241" title="Number of partitions of n into 5 parts such that every i-th smallest part (counted with multiplicity) is different from i.">A244241</a> * <a href="/A244243" title="Number of partitions of n into 7 parts such that every i-th smallest part (counted with multiplicity) is different from i.">A244243</a> <a href="/A244244" title="Number of partitions of n into 8 parts such that every i-th smallest part (counted with multiplicity) is different from i.">A244244</a> <a href="/A244245" title="Number of partitions of n into 9 parts such that every i-th smallest part (counted with multiplicity) is different from i.">A244245</a></div> </div> </div> <div class=section> <div class=sectname>KEYWORD</div> <div class=sectbody> <div class=sectline><span title="a sequence of nonnegative numbers">nonn</span></div> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <div class=sectline><a href="/wiki/User:Alois_P._Heinz">Alois P. Heinz</a>, Jun 23 2014</div> </div> </div> <div class=section> <div class=sectname>STATUS</div> <div class=sectbody> <div class=sectline>approved</div> </div> </div> </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 April 10 18:08 EDT 2025. Contains 382674 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>