Template:Boolf weight triangle 5

Template:Diagonal split header	$0$	$\frac{1}{32}$	$\frac{1}{16}$	$\frac{3}{32}$	$\frac{1}{8}$	$\frac{5}{32}$	$\frac{3}{16}$	$\frac{7}{32}$	$\frac{1}{4}$	$\frac{9}{32}$	$\frac{5}{16}$	$\frac{11}{32}$	$\frac{3}{8}$	$\frac{13}{32}$	$\frac{7}{16}$	$\frac{15}{32}$	$\frac{1}{2}$	$\frac{17}{32}$	$\frac{9}{16}$	$\frac{19}{32}$	$\frac{5}{8}$	$\frac{21}{32}$	$\frac{11}{16}$	$\frac{23}{32}$	$\frac{3}{4}$	$\frac{25}{32}$	$\frac{13}{16}$	$\frac{27}{32}$	$\frac{7}{8}$	$\frac{29}{32}$	$\frac{15}{16}$	$\frac{31}{32}$	$1$	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}}}

Template:Diagonal split header	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}}}

Template:Diagonal split header	$\frac{1}{32}$	$\frac{1}{16}$	$\frac{1}{8}$	$\frac{1}{4}$	$\frac{1}{2}$	$1$	sums
0						{{{2}}}	{{{2}}}
1					{{{4}}}	{{{5}}}
2				{{{7}}}	{{{8}}}	{{{10}}}
3			{{{12}}}	{{{13}}}	{{{15}}}	{{{19}}}
4		{{{21}}}	{{{22}}}	{{{24}}}	{{{28}}}	{{{36}}}
5	{{{38}}}	{{{39}}}	{{{41}}}	{{{45}}}	{{{53}}}	{{{69}}}

w	0	1	2	3...4	5...8	9...16	17...32	sums
Template:Diagonal split header	-1	0	1	2	3	4	5
0	{{{1}}}	{{{2}}}
1	{{{3}}}	{{{4}}}	{{{5}}}
2	{{{6}}}	{{{7}}}	{{{8}}}
3	{{{11}}}	{{{12}}}	{{{13}}}
4	{{{20}}}	{{{21}}}	{{{22}}}
5	{{{37}}}	{{{38}}}	{{{39}}}

Template:Collapsible END Template:Collapsible START 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}}}],
[{{{4}}}, {{{5}}}],
[{{{7}}}, {{{8}}}, {{{10}}}],
[{{{12}}}, {{{13}}}, {{{15}}}, {{{19}}}],
[{{{21}}}, {{{22}}}, {{{24}}}, {{{28}}}, {{{36}}}],
[{{{38}}}, {{{39}}}, {{{41}}}, {{{45}}}, {{{53}}}, {{{69}}}]

row sums of unit fractions: [{{{2}}}, , , , , ]

---

merged rows:
[{{{1}}}, {{{2}}}],
[{{{3}}}, {{{4}}}, {{{5}}}],
[{{{6}}}, {{{7}}}, {{{8}}}, ],
[{{{11}}}, {{{12}}}, {{{13}}}, , ],
[{{{20}}}, {{{21}}}, {{{22}}}, , , ],
[{{{37}}}, {{{38}}}, {{{39}}}, , , , ]

merged diagonal:   (k = arity)
[{{{2}}}, {{{5}}}, , , , ] Template:Collapsible END

---

see e.g. Template:Tl

Template:Tl is for arities up to 4. (For some cases the calculation for arity 5 is not feasible.)