[Nov 1, 2020 Programming Adventures]
[Nov 1, 2020 Programming Adventures]
In[]:=
f[n_]:=f[n-1]+f[n-2]
In[]:=
f[1]=f[2]=1
Out[]=
1
In[]:=
Array[f,20]
Out[]=
{1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765}
In[]:=
f[n_]:=f[n]=f[f[n-1]]+f[n-f[n-1]]
In[]:=
Array[f,20]
Out[]=
{1,1,2,2,3,4,4,4,5,6,7,7,8,8,8,8,9,10,11,12}
In[]:=
Table[f[n]-n/2,{n,200}]
Out[]=
,0,,0,,1,,0,,1,,1,,1,,0,,1,,2,,2,,2,,2,,2,,1,,0,,1,,2,,2,,3,,3,,4,,4,,3,,4,,4,,3,,3,,2,,2,,1,,0,,1,,2,,3,,3,,4,,4,,5,,5,,6,,6,,5,,6,,6,,7,,7,,6,,7,,7,,6,,6,,5,,6,,6,,5,,5,,4,,4,,3,,3,,2,,1,,0,,1,,2,,3,,3,,4,,5,,5,,6,,7,,7,,8,,8,,8,,8,,8,,9,,9,,10,,10,,11,,11,,10,,11,,11,,12,,12,,11,,12,,12,,11,,11,,10,,11,,11,,12,,12
1
2
1
2
1
2
1
2
1
2
3
2
3
2
1
2
1
2
3
2
3
2
5
2
5
2
3
2
3
2
1
2
1
2
3
2
5
2
5
2
7
2
7
2
7
2
7
2
7
2
7
2
7
2
7
2
5
2
5
2
3
2
1
2
1
2
3
2
5
2
5
2
7
2
9
2
9
2
11
2
11
2
11
2
11
2
11
2
13
2
13
2
13
2
13
2
13
2
13
2
13
2
13
2
11
2
11
2
11
2
11
2
11
2
9
2
9
2
7
2
5
2
5
2
3
2
1
2
1
2
3
2
5
2
7
2
7
2
9
2
11
2
11
2
13
2
13
2
15
2
15
2
17
2
17
2
15
2
17
2
19
2
19
2
21
2
21
2
21
2
21
2
21
2
23
2
23
2
23
2
23
2
23
2
23
2
23
2
23
2
21
2
21
2
23
2
23
2
23
2
In[]:=
ListLinePlot[%]
Out[]=
In[]:=
Clear[f]
In[]:=
f[n_]:=f[n]=f[n-f[n-1]]+f[n-f[n-2]]
In[]:=
f[1]=f[2]=1;
In[]:=
ListLinePlot[Table[f[n]-n/2,{n,200}],PlotRangeAll]
Out[]=
In[]:=
ListLinePlot[Table[f[n]-n/2,{n,1000}],PlotRangeAll]
Out[]=
In[]:=
Histogram[Table[f[n]-n/2,{n,1000}],{1}]
Out[]=
In[]:=
ListLinePlot[FoldList[Max,Table[f[n]-n/2,{n,1000}]],PlotRangeAll]
Out[]=
In[]:=
ListLinePlot[FoldList[Max,Table[f[n]-n/2,{n,10000}]],PlotRangeAll]
Out[]=
In[]:=
Histogram[Table[f[n]-n/2,{n,10000}],{1}]
Out[]=
In[]:=
Table[{n-f[n-1],n-f[n-2]},{n,3,10}]
Out[]=
{{2,2},{2,3},{2,3},{3,3},{3,4},{3,4},{4,4},{4,5}}
In[]:=
ListLinePlot[Transpose[Table[{n-f[n-1],n-f[n-2]},{n,3,100}]]]
Out[]=
Number of possible paths to the leaves from a given point is the Fibonacci number...
Weird function
Weird function
Another case
Another case