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# Template:Sierpiński's triangle (Pascal's triangle mod 2)

Sierpiński's triangle (Pascal's triangle mod
 2
)

 n
${\displaystyle {\begin{array}{l}\displaystyle {[{\rm {row}}(n)]_{2}=\left[\sum _{i=0}^{n}{\bigg (}{\binom {n}{i}}~{\bmod {~}}2{\bigg )}~2^{i}\right]_{2}=\left[\prod _{i=0}^{\lfloor \log _{2}(n)\rfloor }{\rm {F}}_{i}^{(\lfloor {\frac {n}{2^{i}}}\rfloor ~{\bmod {~}}2)}\right]_{2}=\left[\prod _{i=0}^{\lfloor \log _{2}(n)\rfloor }(2^{2^{i}}+1)^{(\lfloor {\frac {n}{2^{i}}}\rfloor ~{\bmod {~}}2)}\right]_{2}}\end{array}}}$
 [row(n)]10
0 1 1
1 1 1 3
2 1 0 1 5
3 1 1 1 1 15
4 1 0 0 0 1 17
5 1 1 0 0 1 1 51
6 1 0 1 0 1 0 1 85
7 1 1 1 1 1 1 1 1 255
8 1 0 0 0 0 0 0 0 1 257
9 1 1 0 0 0 0 0 0 1 1 771
10 1 0 1 0 0 0 0 0 1 0 1 1285
11 1 1 1 1 0 0 0 0 1 1 1 1 3855
12 1 0 0 0 1 0 0 0 1 0 0 0 1 4369
13 1 1 0 0 1 1 0 0 1 1 0 0 1 1 13107
14 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 21845
15 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 65535
16 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 65537
17 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 196611
18 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 327685
19 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 983055
20 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1114129
21 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 3342387
22 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 5570645
23 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 16711935
24 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 16843009
25 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 50529027
26 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 84215045
27 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 252645135
28 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 286331153
29 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 858993459
30 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1431655765
31 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4294967295
32 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4294967297
 i =
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