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Pascal's triangle |
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0 |
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1 |
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1 |
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1 |
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1 |
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2 |
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1 |
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2 |
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1 |
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3 |
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1 |
|
3 |
|
3 |
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1 |
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4 |
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1 |
|
4 |
|
6 |
|
4 |
|
1 |
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|
5 |
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1 |
|
5 |
|
10 |
|
10 |
|
5 |
|
1 |
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|
6 |
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1 |
|
6 |
|
15 |
|
20 |
|
15 |
|
6 |
|
1 |
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|
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7 |
|
|
1 |
|
7 |
|
21 |
|
35 |
|
35 |
|
21 |
|
7 |
|
1 |
|
|
|
|
|
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|
8 |
|
1 |
|
8 |
|
28 |
|
56 |
|
70 |
|
56 |
|
28 |
|
8 |
|
1 |
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Automaton shape |
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0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
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0 |
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1 |
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1 |
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1 |
1 |
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2 |
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1 |
2 |
1 |
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3 |
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1 |
3 |
3 |
1 |
|
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4 |
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1 |
4 |
6 |
4 |
1 |
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5 |
|
1 |
5 |
10 |
10 |
5 |
1 |
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|
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|
6 |
|
1 |
6 |
15 |
20 |
15 |
6 |
1 |
|
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|
|
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|
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|
7 |
|
1 |
7 |
21 |
35 |
35 |
21 |
7 |
1 |
|
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|
|
|
|
|
|
|
|
|
|
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|
8 |
|
1 |
8 |
28 |
56 |
70 |
56 |
28 |
8 |
1 |
|
|
|
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|
|
|
|
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|
|
|
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|
|
9 |
|
1 |
9 |
36 |
84 |
126 |
126 |
84 |
36 |
9 |
1 |
|
|
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|
|
|
|
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|
|
|
|
|
|
10 |
|
1 |
10 |
45 |
120 |
210 |
252 |
210 |
120 |
45 |
10 |
1 |
|
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|
|
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|
|
|
|
|
|
11 |
|
1 |
11 |
55 |
165 |
330 |
462 |
462 |
330 |
165 |
55 |
11 |
1 |
|
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|
|
|
|
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|
|
|
|
12 |
|
1 |
12 |
66 |
220 |
495 |
792 |
924 |
792 |
495 |
220 |
66 |
12 |
1 |
|
|
|
|
|
|
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|
|
|
|
13 |
|
1 |
13 |
78 |
286 |
715 |
1287 |
1716 |
1716 |
1287 |
715 |
286 |
78 |
13 |
1 |
|
|
|
|
|
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|
|
|
|
14 |
|
1 |
14 |
91 |
364 |
1001 |
2002 |
3003 |
3432 |
3003 |
2002 |
1001 |
364 |
91 |
14 |
1 |
|
|
|
|
|
|
|
|
|
15 |
|
1 |
15 |
105 |
455 |
1365 |
3003 |
5005 |
6435 |
6435 |
5005 |
3003 |
1365 |
455 |
105 |
15 |
1 |
|
|
|
|
|
|
|
|
16 |
|
1 |
16 |
120 |
560 |
1820 |
4368 |
8008 |
11440 |
12870 |
11440 |
8008 |
4368 |
1820 |
560 |
120 |
16 |
1 |
|
|
|
|
|
|
|
17 |
|
1 |
17 |
136 |
680 |
2380 |
6188 |
12376 |
19448 |
24310 |
24310 |
19448 |
12376 |
6188 |
2380 |
680 |
136 |
17 |
1 |
|
|
|
|
|
|
18 |
|
1 |
18 |
153 |
816 |
3060 |
8568 |
18564 |
31824 |
43758 |
48620 |
43758 |
31824 |
18564 |
8568 |
3060 |
816 |
153 |
18 |
1 |
|
|
|
|
|
19 |
|
1 |
19 |
171 |
969 |
3876 |
11628 |
27132 |
50388 |
75582 |
92378 |
92378 |
75582 |
50388 |
27132 |
11628 |
3876 |
969 |
171 |
19 |
1 |
|
|
|
|
20 |
|
1 |
20 |
190 |
1140 |
4845 |
15504 |
38760 |
77520 |
125970 |
167960 |
184756 |
167960 |
125970 |
77520 |
38760 |
15504 |
4845 |
1140 |
190 |
20 |
1 |
|
|
|
21 |
|
1 |
21 |
210 |
1330 |
5985 |
20349 |
54264 |
116280 |
203490 |
293930 |
352716 |
352716 |
293930 |
203490 |
116280 |
54264 |
20349 |
5985 |
1330 |
210 |
21 |
1 |
|
|
22 |
|
1 |
22 |
231 |
1540 |
7315 |
26334 |
74613 |
170544 |
319770 |
497420 |
646646 |
705432 |
646646 |
497420 |
319770 |
170544 |
74613 |
26334 |
7315 |
1540 |
231 |
22 |
1 |
|
23 |
|
1 |
23 |
253 |
1771 |
8855 |
33649 |
100947 |
245157 |
490314 |
817190 |
1144066 |
1352078 |
1352078 |
1144066 |
817190 |
490314 |
245157 |
100947 |
33649 |
8855 |
1771 |
253 |
23 |
1 |
|
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|
Mod 2 |
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0 |
|
1 |
|
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1 |
|
1 |
1 |
|
|
|
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|
|
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|
|
|
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|
|
|
|
2 |
|
1 |
0 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
|
1 |
1 |
1 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
|
1 |
0 |
0 |
0 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5 |
|
1 |
1 |
0 |
0 |
1 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
6 |
|
1 |
0 |
1 |
0 |
1 |
0 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
7 |
|
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
8 |
|
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
9 |
|
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
10 |
|
1 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
11 |
|
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
12 |
|
1 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
|
|
|
|
|
|
|
|
|
|
|
13 |
|
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
|
|
|
|
|
|
|
|
|
|
14 |
|
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
|
|
|
|
|
|
|
|
|
15 |
|
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
|
|
|
|
|
|
|
|
16 |
|
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
Mod 3 |
|
|
|
|
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|
|
|
|
|
|
|
0 |
|
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
|
1 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
|
1 |
2 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
|
1 |
0 |
0 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
|
1 |
1 |
0 |
1 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5 |
|
1 |
2 |
1 |
1 |
2 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
6 |
|
1 |
0 |
0 |
2 |
0 |
0 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
7 |
|
1 |
1 |
0 |
2 |
2 |
0 |
1 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
8 |
|
1 |
2 |
1 |
2 |
1 |
2 |
1 |
2 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
9 |
|
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
10 |
|
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
11 |
|
1 |
2 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
2 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
12 |
|
1 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
|
|
|
|
|
|
|
|
|
|
|
13 |
|
1 |
1 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
1 |
1 |
|
|
|
|
|
|
|
|
|
|
14 |
|
1 |
2 |
1 |
1 |
2 |
1 |
0 |
0 |
0 |
1 |
2 |
1 |
1 |
2 |
1 |
|
|
|
|
|
|
|
|
|
15 |
|
1 |
0 |
0 |
2 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
2 |
0 |
0 |
1 |
|
|
|
|
|
|
|
|
16 |
|
1 |
1 |
0 |
2 |
2 |
0 |
1 |
1 |
0 |
1 |
1 |
0 |
2 |
2 |
0 |
1 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
|
|