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