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A368465 - 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>A368465 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A368465" 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=%2fA368465">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="A368465 - 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> A368465 </div> <div class=seqname> Number of even terms in each row of the iterates of the Christmas tree pattern map (<a href="/A367508" title="Iterates of the Christmas tree pattern map, read by rows, with leading zeros removed and interpreted as decimal numbers (see...">A367508</a>). </div> </div> <div class=scorerefs> 4 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 2, 1, 4, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 3, 1, 5, 1, 1, 2, 1, 1, 2, 1, 2, 1, 4, 1, 1, 2, 1, 1, 2, 1, 2, 1, 4, 1, 1, 2, 1, 2, 1, 4, 1, 2, 1, 4, 1, 4, 1, 6, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3</div> <div class=seqdatalinks> (<a href="/A368465/list">list</a>; <a href="/A368465/graph">graph</a>; <a href="/search?q=A368465+-id:A368465">refs</a>; <a href="/A368465/listen">listen</a>; <a href="/history?seq=A368465">history</a>; <a href="/search?q=id:A368465&fmt=text">text</a>; <a href="/A368465/internal">internal format</a>) </div> </div> </div> <div class=entry> <div class=section> <div class=sectname>OFFSET</div> <div class=sectbody> <div class=sectline>1,5</div> </div> </div> <div class=section> <div class=sectname>COMMENTS</div> <div class=sectbody> <div class=sectline>See <a href="/A367508" title="Iterates of the Christmas tree pattern map, read by rows, with leading zeros removed and interpreted as decimal numbers (see...">A367508</a> for the description of the Christmas tree patterns, references and links.</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline>Paolo Xausa, <a href="/A368465/b368465.txt">Table of n, a(n) for n = 1..13494</a> (first 15 orders).</div> </div> </div> <div class=section> <div class=sectname>EXAMPLE</div> <div class=sectbody> <div class=sectline>The first 4 tree pattern orders are shown below (left), with the corresponding number of even terms on the right.</div> <div class=sectline>.</div> <div class=sectline>Order 1: |</div> <div class=sectline> 0 1 | 1</div> <div class=sectline> |</div> <div class=sectline>Order 2: |</div> <div class=sectline> 10 | 1</div> <div class=sectline> 00 01 11 | 1</div> <div class=sectline> |</div> <div class=sectline>Order 3: |</div> <div class=sectline> 100 101 | 1</div> <div class=sectline> 010 110 | 2</div> <div class=sectline> 000 001 011 111 | 1</div> <div class=sectline> |</div> <div class=sectline>Order 4: |</div> <div class=sectline> 1010 | 1</div> <div class=sectline> 1000 1001 1011 | 1</div> <div class=sectline> 1100 | 1</div> <div class=sectline> 0100 0101 1101 | 1</div> <div class=sectline> 0010 0110 1110 | 3</div> <div class=sectline> 0000 0001 0011 0111 1111 | 1</div> <div class=sectline>.</div> </div> </div> <div class=section> <div class=sectname>MATHEMATICA</div> <div class=sectbody> <div class=sectline>With[{imax=8}, Map[Total, Map[Mod[FromDigits[#]+1, 2]&, NestList[Map[Delete[{If[Length[#]>1, Map[#<>"0"&, Rest[#]], Nothing], Join[{#[[1]]<>"0"}, Map[#<>"1"&, #]]}, 0]&], {{"0", "1"}}, imax-1], {3}], {2}]] (* Generates terms up to order 8 *)</div> </div> </div> <div class=section> <div class=sectname>PROG</div> <div class=sectbody> <div class=sectline>(Python)</div> <div class=sectline>from itertools import islice</div> <div class=sectline>from functools import reduce</div> <div class=sectline>def uniq(r): return reduce(lambda u, e: u if e in u else u+[e], r, [])</div> <div class=sectline>def agen(): # generator of terms</div> <div class=sectline> R = [["0", "1"]]</div> <div class=sectline> while R:</div> <div class=sectline> r = R.pop(0)</div> <div class=sectline> yield sum(b[-1] == '0' for b in r)</div> <div class=sectline> if len(r) > 1: R.append(uniq([r[k]+"0" for k in range(1, len(r))]))</div> <div class=sectline> R.append(uniq([r[0]+"0", r[0]+"1"] + [r[k]+"1" for k in range(1, len(r))]))</div> <div class=sectline>print(list(islice(agen(), 88))) # <a href="/wiki/User:Michael_S._Branicky">Michael S. Branicky</a>, Dec 25 2023</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A367508" title="Iterates of the Christmas tree pattern map, read by rows, with leading zeros removed and interpreted as decimal numbers (see...">A367508</a>, <a href="/A368463" title="Parity of the iterates of the Christmas tree pattern map (A367508), read by rows.">A368463</a>, <a href="/A368464" title="Number of odd terms in each row of the iterates of the Christmas tree pattern map (A367508).">A368464</a>.</div> <div class=sectline>Sequence in context: <a href="/A333769" title="Irregular triangle read by rows where row k is the sequence of run-lengths of the k-th composition in standard order.">A333769</a> <a href="/A259396" title="Length of runs of identical terms in A080378.">A259396</a> <a href="/A328672" title="Number of integer partitions of n with relatively prime parts in which no two distinct parts are relatively prime.">A328672</a> * <a href="/A378222" title="Number of ordered factorizations of the odd part of n into factors > 1.">A378222</a> <a href="/A325355" title="One plus the number of steps applying A325351 (Heinz number of augmented differences of reversed prime indices) to reach a f...">A325355</a> <a href="/A219093" title="Denominator of the least reduced fraction b/c > 1 using divisors b and c of n.">A219093</a></div> <div class=sectline>Adjacent sequences: <a href="/A368462" title="Prime averages of first k odd primes for some k.">A368462</a> <a href="/A368463" title="Parity of the iterates of the Christmas tree pattern map (A367508), read by rows.">A368463</a> <a href="/A368464" title="Number of odd terms in each row of the iterates of the Christmas tree pattern map (A367508).">A368464</a> * <a href="/A368466" title="a(n) = Sum_{k=0..n} 2^k * k^n.">A368466</a> <a href="/A368467" title="a(n) = Sum_{k=0..n} (-1)^k * binomial(2*n,k) * binomial(4*n,n-k).">A368467</a> <a href="/A368468" title="a(n) is the number of exponentially odd divisors of the n-th exponentially odd number.">A368468</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:Paolo_Xausa">Paolo Xausa</a>, Dec 25 2023</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 March 9 11:46 EDT 2025. Contains 381557 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>