<div class="thumb tright"><div class="thumbinner" style="width:222px;"><a href="//commons.wikimedia.org/wiki/File:Partitions_of_6-set_with_3_singletons.svg" class="image"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/82/Partitions_of_6-set_with_3_singletons.svg/220px-Partitions_of_6-set_with_3_singletons.svg.png" decoding="async" width="220" height="321" class="thumbimage" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/8/82/Partitions_of_6-set_with_3_singletons.svg/330px-Partitions_of_6-set_with_3_singletons.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/8/82/Partitions_of_6-set_with_3_singletons.svg/440px-Partitions_of_6-set_with_3_singletons.svg.png 2x" data-file-width="462" data-file-height="675"></a>  <div class="thumbcaption"><div class="magnify"><a href="//commons.wikimedia.org/wiki/File:Partitions_of_6-set_with_3_singletons.svg" class="internal" title="Enlarge"></a></div>The actually 20 partitions of a 6-set that have 3 singletons count only as 3 in this triangle.</div></div></div> 
<p>Illustration of the triangle <span style="white-space:nowrap"><a href="https://en.wikipedia.org/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="Sloane's"><img alt="Sloane's" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/OEISicon_light.svg/11px-OEISicon_light.svg.png" decoding="async" width="11" height="15" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/OEISicon_light.svg/17px-OEISicon_light.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/OEISicon_light.svg/22px-OEISicon_light.svg.png 2x" data-file-width="409" data-file-height="556"></a> <a href="//oeis.org/A152176" class="extiw" title="oeis:A152176">A152176</a></span> with the row sums <span style="white-space:nowrap"><a href="https://en.wikipedia.org/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="Sloane's"><img alt="Sloane's" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/OEISicon_light.svg/11px-OEISicon_light.svg.png" decoding="async" width="11" height="15" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/OEISicon_light.svg/17px-OEISicon_light.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/OEISicon_light.svg/22px-OEISicon_light.svg.png 2x" data-file-width="409" data-file-height="556"></a> <a href="//oeis.org/A084708" class="extiw" title="oeis:A084708">A084708</a></span> on the right
</p><p>The partitions of an <i>n</i>-set with <i>k</i> blocks are counted up to rotation and reflection.
</p><p>Compare: <a href="https://en.wikiversity.org/wiki/Partition_related_number_triangles" class="extiw" title="v:Partition related number triangles">v:Partition related number triangles </a>
</p><p>These are the possible patterns of <i>free <a href="https://en.wikipedia.org/wiki/Necklace_(combinatorics)" class="extiw" title="w:Necklace (combinatorics)">necklaces</a></i> (or <i>bracelets</i>)<br></p>
of length <i>n</i> <small>(from 1 top to bottom)</small> with <i>k</i> <small>(from 1 left to right)</small> different colors.
<table><tbody><tr><td style="padding: 15px;"><a href="//commons.wikimedia.org/wiki/File:Watchduck.svg" class="image"><img alt="Watchduck.svg" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Watchduck.svg/40px-Watchduck.svg.png" decoding="async" width="40" height="46" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Watchduck.svg/60px-Watchduck.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Watchduck.svg/80px-Watchduck.svg.png 2x" data-file-width="703" data-file-height="806"></a>
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<td><a href="//commons.wikimedia.org/wiki/User:Watchduck" title="User:Watchduck">Watchduck</a><br><span style="color: gray; font-size: 80%;">You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".</span>
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<span class="int-own-work" lang="en">Own work</span>