Template:Tiara 5

integer weight

w a 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 sums 0 {{{1}}} {{{2}}} 1 {{{3}}} {{{4}}} {{{5}}} 2 {{{6}}} {{{7}}} {{{8}}} {{{9}}} {{{10}}} 3 {{{11}}} {{{12}}} {{{13}}} {{{14}}} {{{15}}} {{{16}}} {{{17}}} {{{18}}} {{{19}}} 4 {{{20}}} {{{21}}} {{{22}}} {{{23}}} {{{24}}} {{{25}}} {{{26}}} {{{27}}} {{{28}}} {{{29}}} {{{30}}} {{{31}}} {{{32}}} {{{33}}} {{{34}}} {{{35}}} {{{36}}} 5 {{{37}}} {{{38}}} {{{39}}} {{{40}}} {{{41}}} {{{42}}} {{{43}}} {{{44}}} {{{45}}} {{{46}}} {{{47}}} {{{48}}} {{{49}}} {{{50}}} {{{51}}} {{{52}}} {{{53}}} {{{54}}} {{{55}}} {{{56}}} {{{57}}} {{{58}}} {{{59}}} {{{60}}} {{{61}}} {{{62}}} {{{63}}} {{{64}}} {{{65}}} {{{66}}} {{{67}}} {{{68}}} {{{69}}}

rational weight

w a $0$ ${\frac {1}{32}}$ ${\frac {1}{16}}$ ${\frac {3}{32}}$ ${\frac {1}{8}}$ ${\frac {5}{32}}$ ${\frac {3}{16}}$ ${\frac {7}{32}}$ ${\frac {1}{4}}$ ${\frac {9}{32}}$ ${\frac {5}{16}}$ ${\frac {11}{32}}$ ${\frac {3}{8}}$ ${\frac {13}{32}}$ ${\frac {7}{16}}$ ${\frac {15}{32}}$ ${\frac {1}{2}}$ ${\frac {17}{32}}$ ${\frac {9}{16}}$ ${\frac {19}{32}}$ ${\frac {5}{8}}$ ${\frac {21}{32}}$ ${\frac {11}{16}}$ ${\frac {23}{32}}$ ${\frac {3}{4}}$ ${\frac {25}{32}}$ ${\frac {13}{16}}$ ${\frac {27}{32}}$ ${\frac {7}{8}}$ ${\frac {29}{32}}$ ${\frac {15}{16}}$ ${\frac {31}{32}}$ $1$ sums 0 {{{1}}} {{{2}}} 1 {{{3}}} {{{4}}} {{{5}}} 2 {{{6}}} {{{7}}} {{{8}}} {{{9}}} {{{10}}} 3 {{{11}}} {{{12}}} {{{13}}} {{{14}}} {{{15}}} {{{16}}} {{{17}}} {{{18}}} {{{19}}} 4 {{{20}}} {{{21}}} {{{22}}} {{{23}}} {{{24}}} {{{25}}} {{{26}}} {{{27}}} {{{28}}} {{{29}}} {{{30}}} {{{31}}} {{{32}}} {{{33}}} {{{34}}} {{{35}}} {{{36}}} 5 {{{37}}} {{{38}}} {{{39}}} {{{40}}} {{{41}}} {{{42}}} {{{43}}} {{{44}}} {{{45}}} {{{46}}} {{{47}}} {{{48}}} {{{49}}} {{{50}}} {{{51}}} {{{52}}} {{{53}}} {{{54}}} {{{55}}} {{{56}}} {{{57}}} {{{58}}} {{{59}}} {{{60}}} {{{61}}} {{{62}}} {{{63}}} {{{64}}} {{{65}}} {{{66}}} {{{67}}} {{{68}}} {{{69}}}

unit fractions
w a $1$ ${\frac {1}{2}}$ ${\frac {1}{4}}$ ${\frac {1}{8}}$ ${\frac {1}{16}}$ ${\frac {1}{32}}$ sums 0 {{{2}}} {{{2}}} 1 {{{5}}} {{{4}}} 2 {{{10}}} {{{8}}} {{{7}}} 3 {{{19}}} {{{15}}} {{{13}}} {{{12}}} 4 {{{36}}} {{{28}}} {{{24}}} {{{22}}} {{{21}}} 5 {{{69}}} {{{53}}} {{{45}}} {{{41}}} {{{39}}} {{{38}}}

plain text

rows: [{{{1}}}, {{{2}}}], [{{{3}}}, {{{4}}}, {{{5}}}], [{{{6}}}, {{{7}}}, {{{8}}}, {{{9}}}, {{{10}}}], [{{{11}}}, {{{12}}}, {{{13}}}, {{{14}}}, {{{15}}}, {{{16}}}, {{{17}}}, {{{18}}}, {{{19}}}], [{{{20}}}, {{{21}}}, {{{22}}}, {{{23}}}, {{{24}}}, {{{25}}}, {{{26}}}, {{{27}}}, {{{28}}}, {{{29}}}, {{{30}}}, {{{31}}}, {{{32}}}, {{{33}}}, {{{34}}}, {{{35}}}, {{{36}}}], [{{{37}}}, {{{38}}}, {{{39}}}, {{{40}}}, {{{41}}}, {{{42}}}, {{{43}}}, {{{44}}}, {{{45}}}, {{{46}}}, {{{47}}}, {{{48}}}, {{{49}}}, {{{50}}}, {{{51}}}, {{{52}}}, {{{53}}}, {{{54}}}, {{{55}}}, {{{56}}}, {{{57}}}, {{{58}}}, {{{59}}}, {{{60}}}, {{{61}}}, {{{62}}}, {{{63}}}, {{{64}}}, {{{65}}}, {{{66}}}, {{{67}}}, {{{68}}}, {{{69}}}] central values:   (rational weight = 1/2) [{{{4}}}, {{{8}}}, {{{15}}}, {{{28}}}, {{{53}}}] diagonal:   (integer weight = arity) [{{{1}}}, {{{4}}}, {{{8}}}, {{{14}}}, {{{24}}}, {{{42}}}] row sums: [, , , , , ] unit fractions: [{{{2}}}], [{{{5}}}, {{{4}}}], [{{{10}}}, {{{8}}}, {{{7}}}], [{{{19}}}, {{{15}}}, {{{13}}}, {{{12}}}], [{{{36}}}, {{{28}}}, {{{24}}}, {{{22}}}, {{{21}}}], [{{{69}}}, {{{53}}}, {{{45}}}, {{{41}}}, {{{39}}}, {{{38}}}] row sums of unit fractions: [{{{2}}}, , , , , ]

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see e.g. {{Tiara pair Onyx/wave}}

{{Tiara 4}} is for arities up to 4. (For some cases the calculation for arity 5 is not feasible.)