Template:Number of relations

Number of n-element binary relations of different types
Elements	Any	Transitive	Reflexive	Symmetric	Preorder	Partial order	Total preorder	Total order	Equivalence relation
0	1	1	1	1	1	1	1	1	1
1	2	2	1	2	1	1	1	1	1
2	16	13	4	8	4	3	3	2	2
3	512	171	64	64	29	19	13	6	5
4	65,536	3,994	4,096	1,024	355	219	75	24	15
n	2^n²		2ⁿ⁽ⁿ⁻¹⁾	2^n(n+1)/2			∑ⁿ _k=0 k!S(n, k)	n!	∑ⁿ _k=0 S(n, k)
OEIS	A002416	A006905	A053763	A006125	A000798	A001035	A000670	A000142	A000110