In[]:=
ResourceFunction["TupleIndex"][ResourceFunction["TupleIndex"]/@{{1,2,3},{4,3},{5,5}}]
Out[]=
54377
In[]:=
ResourceFunction["TupleIndex"][ResourceFunction["TupleIndex"]/@{{3,2,5},{3,5,4},{1,4},{2,6},{7,8}}]
Out[]=
136923635811
In[]:=
FromDigits[Flatten[{{3,2,5},{3,5,4},{1,4},{2,6},{7,8}}]-1,8]
Out[]=
18833224567
In[]:=
ResourceFunction["TupleFromIndex"][234235,3]
Out[]=
{58,61,58}
In[]:=
ResourceFunction["TupleIndex"]/@Tuples[Range[0,1],5]
Out[]=
{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}
In[]:=
ResourceFunction["TupleIndex"]/@Tuples[Range[0,2],4]
Out[]=
{1,2,17,3,4,18,19,20,21,5,6,22,7,8,23,24,25,26,27,28,29,30,31,32,33,34,35,9,10,36,11,12,37,38,39,40,13,14,41,15,16,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81}
In[]:=
ListLinePlot[%]
Out[]=
20
40
60
80
20
40
60
80
In[]:=
ResourceFunction["TupleIndex"]/@Tuples[Range[0,3],2]
Out[]=
{1,2,5,10,3,4,6,11,7,8,9,12,13,14,15,16}
In[]:=
ResourceFunction["TupleIndex"]/@SortBy[Tuples[Range[0,3],2],{Max,Reverse}]
Out[]=
{1,3,2,4,7,8,5,6,9,13,14,15,10,11,12,16}
In[]:=
ListLinePlot[%]
Out[]=
5
10
15
5
10
15
In[]:=
ResourceFunction["TupleIndex"][{20,30,40}]
Out[]=
65651
In[]:=
Table[ResourceFunction["TupleIndex"][{1,1,n}],{n,20}]
Out[]=
{8,15,36,75,138,231,360,531,750,1023,1356,1755,2226,2775,3408,4131,4950,5871,6900,8043}
In[]:=
ListLinePlot[%]
Out[]=
5
10
15
20
2000
4000
6000
8000
In[]:=
Ratios[%86]//N
Out[]=
{1.875,2.4,2.08333,1.84,1.67391,1.55844,1.475,1.41243,1.364,1.32551,1.29425,1.26838,1.24663,1.22811,1.21215,1.19826,1.18606,1.17527,1.16565}
In[]:=
ListLinePlot[%]
Out[]=
5
10
15
0.5
1.0
1.5
2.0
2.5
In[]:=
ResourceFunction["TupleIndex"][{0,1,1}]
Out[]=
4
In[]:=
ResourceFunction["TupleIndex"][{0,1,1}+1]
Out[]=
18
In[]:=
BellB[12]
Out[]=
4213597
{{2,3}}{{3,2}}
In[]:=
ResourceFunction["RandomWolframModel"][{{2,2}}{{4,2}},12]
Out[]=
{{1,2},{3,4}}{{1,2},{3,1},{5,4},{6,4}}
Asymptotic
{{nl,2}}->{{nr,2}}
BellB[2(nl+nr)]/(nl!nr!)
In[]:=
BellB[2(2+nr)]/(2!nr!)
Out[]=
BellB[2(2+nr)]
2nr!
In[]:=
Asymptotic[%,{nr,Infinity,2}]
Out[]=
nr(1-Log[nr])

-
1
24
3/2
nr
2π
+
1
2
nr
2π
BellB[2(2+nr)]
In[]:=
Asymptotic[BellB[n],{n,Infinity,2}]
Out[]=
BellB[n]
{{nl,3}}->{{nr,3}}