Pascal's triangle
0 1
1 1 1
2 1 2 1
 
 
3 1 3 3 1  
4 1 4 6 4 1
5 1 5 10 10 5 1
6 1 6 15 20 15 6 1
7 1 7 21 35 35 21 7 1
8 1 8 28 56 70 56 28 8 1
Automaton shape
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0 1
1 1 1
2 1 2 1
3 1 3 3 1
 
 
4 1 4 6 4 1  
5 1 5 10 10 5 1
6 1 6 15 20 15 6 1
7 1 7 21 35 35 21 7 1
8 1 8 28 56 70 56 28 8 1
9 1 9 36 84 126 126 84 36 9 1
10 1 10 45 120 210 252 210 120 45 10 1
11 1 11 55 165 330 462 462 330 165 55 11 1
12 1 12 66 220 495 792 924 792 495 220 66 12 1
13 1 13 78 286 715 1287 1716 1716 1287 715 286 78 13 1
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
Mod 2
0 1
1 1 1
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
Mod 3
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