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A131877 - 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>A131877 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A131877" 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=%2fA131877">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="A131877 - 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> A131877 </div> <div class=seqname> a(n) = 14*n + 1. </div> </div> <div class=scorerefs> 4 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>1, 15, 29, 43, 57, 71, 85, 99, 113, 127, 141, 155, 169, 183, 197, 211, 225, 239, 253, 267, 281, 295, 309, 323, 337, 351, 365, 379, 393, 407, 421, 435, 449, 463, 477, 491, 505, 519, 533, 547, 561, 575, 589, 603, 617, 631, 645, 659, 673, 687, 701, 715, 729</div> <div class=seqdatalinks> (<a href="/A131877/list">list</a>; <a href="/A131877/graph">graph</a>; <a href="/search?q=A131877+-id:A131877">refs</a>; <a href="/A131877/listen">listen</a>; <a href="/history?seq=A131877">history</a>; <a href="/search?q=id:A131877&fmt=text">text</a>; <a href="/A131877/internal">internal format</a>) </div> </div> </div> <div class=entry> <div class=section> <div class=sectname>OFFSET</div> <div class=sectbody> <div class=sectline>0,2</div> </div> </div> <div class=section> <div class=sectname>COMMENTS</div> <div class=sectbody> <div class=sectline>Left column of triangle <a href="/A131876" title="2*A131873 - 1.">A131876</a>.</div> <div class=sectline>Binomial transform of (1, 14, 0, 0, 0, ...).</div> <div class=sectline>Partial sums give <a href="/A051868" title="16-gonal (or hexadecagonal) numbers: a(n) = n*(7*n-6).">A051868</a>. - <a href="/wiki/User:Leo_Tavares">Leo Tavares</a>, Mar 19 2023</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline><a href="/A131877/b131877.txt">Table of n, a(n) for n=0..52.</a></div> <div class=sectline><a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).</div> </div> </div> <div class=section> <div class=sectname>FORMULA</div> <div class=sectbody> <div class=sectline>a(n) = 14*n + 1.</div> <div class=sectline>From <a href="/wiki/User:Elmo_R._Oliveira">Elmo R. Oliveira</a>, Apr 03 2024: (Start)</div> <div class=sectline>G.f.: (1+13*x)/(1-x)^2.</div> <div class=sectline>E.g.f.: exp(x)*(1 + 14*x).</div> <div class=sectline>a(n) = <a href="/A051868" title="16-gonal (or hexadecagonal) numbers: a(n) = n*(7*n-6).">A051868</a>(n+1) - <a href="/A051868" title="16-gonal (or hexadecagonal) numbers: a(n) = n*(7*n-6).">A051868</a>(n).</div> <div class=sectline>a(n) = 2*a(n-1) - a(n-2) for n >= 2. (End)</div> </div> </div> <div class=section> <div class=sectname>EXAMPLE</div> <div class=sectbody> <div class=sectline>a(2) = 29 = 2*14 + 1.</div> <div class=sectline>a(2) = 29 = (1, 2, 1) dot (1, 14, 0) = (1 + 28 + 0).</div> </div> </div> <div class=section> <div class=sectname>MATHEMATICA</div> <div class=sectbody> <div class=sectline>Range[1, 1000, 14] (* <a href="/wiki/User:Vladimir_Joseph_Stephan_Orlovsky">Vladimir Joseph Stephan Orlovsky</a>, May 31 2011 *)</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A008596" title="Multiples of 14.">A008596</a>, <a href="/A131876" title="2*A131873 - 1.">A131876</a>.</div> <div class=sectline>Cf. <a href="/A051868" title="16-gonal (or hexadecagonal) numbers: a(n) = n*(7*n-6).">A051868</a>.</div> <div class=sectline>Sequence in context: <a href="/A051121" title="Dates at fortnightly intervals starting on Jan 01 of a leap year in the Julian calendar.">A051121</a> <a href="/A001356" title="Dates at fortnightly intervals from Jan 01 in the Julian calendar.">A001356</a> <a href="/A104811" title="Positions of 7 in partition of decimal expansion of Pi A104807.">A104811</a> * <a href="/A354161" title="Index of A354160(n) in A090252.">A354161</a> <a href="/A211324" title="Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and one or three distinct values.">A211324</a> <a href="/A354163" title="Index of A354162(n) in A090252.">A354163</a></div> <div class=sectline>Adjacent sequences: <a href="/A131874" title="a(n) = (7*n^2 + 15*n + 2) / 2.">A131874</a> <a href="/A131875" title="Triangle, A000012 * A131844 as infinite lower triangular matrices.">A131875</a> <a href="/A131876" title="2*A131873 - 1.">A131876</a> * <a href="/A131878" title="a(n) = 7*n^2 + 14*n + 1.">A131878</a> <a href="/A131879" title="Triangle where row n contains the first n positive integers which are coprime to (2^n -1).">A131879</a> <a href="/A131880" title="a(n) = the n-th positive integer which is coprime to (2^n -1). a(n) = the n-th term of row n in triangle A131879.">A131880</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:Gary_W._Adamson">Gary W. Adamson</a>, Jul 22 2007</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 05:25 EDT 2025. Contains 382654 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>