exercise4:
[[0.5 1.  0.  0.  0.  0.  0. ]
 [0.  0.5 1.  0.  0.  0.  0. ]
 [0.  0.  0.5 1.  0.  0.  0. ]
 [0.  0.  0.  0.5 1.  0.  0. ]
 [0.  0.  0.  0.  0.5 1.  0. ]
 [0.  0.  0.  0.  0.  0.5 1. ]
 [0.  0.  0.  0.  0.  0.  0.5]]
0 2.6457513110645907
1 3.7080992435478315
2 5.190134873006674
3 7.210019070709869
4 9.897719118564641
5 13.350115577683214
6 17.519401912148002
7 21.91707866943822
8 25.701745011871733
9 28.067373077793317
10 28.59696258674909
11 27.352399715717063
12 24.74300504224507
13 21.321223716162205
14 17.613705600877044
15 14.026498226207556
16 10.817315001874412
17 8.110613956113234
18 5.931671316287135
19 4.243204781206987
20 2.975964285793769
21 2.0504656801593684
22 1.3903358913161947
23 0.9291352635521786
24 0.6127662275304858
25 0.39926473363533704
26 0.2572829351749574
27 0.16410724384414477
28 0.10369332243738573
29 0.06495050142903132
30 0.04035462788680534
31 0.024884336975687364
32 0.015236997398895289
33 0.009268532887678229
34 0.005603251792664436
35 0.0033678276383234747
36 0.0020132089037425164
37 0.0011972726796862579
38 0.0007085772551226668
39 0.0004174320661424895
40 0.00024484677480743106