A345317 Number of transitive but not symmetric relations on an n-set.

0, 0, 8, 156, 3942, 154100, 9414312, 878218390, 122207682476, 24890747805972, 7307450298831718, 3053521546328889460, 1797003559223742679800, 1476062693867018935173990, 1679239558149570227773844452, 2628225174143857306613215434524, 5626175867513779058706923151723150

Offset: 0

Author

Firdous Ahmad Mala, Oct 02 2021

Keywords

• nonn

Comments

The number of relations on n elements that are symmetric and transitive is the same as the number of equivalence relations on n+1 elements. Consequently, the number of relations that are transitive but not symmetric is obtained by subtracting the terms in the sequence of Bell numbers from that of the sequence of number of labeled transitive relations.

a(n) is even for all n.

Examples

			For n=3, a(3) = A006905(3) - A000110(4) = 171 - 15 = 156.
		

Links

• Des MacHale and Peter MacHale, Relations on Sets, The Mathematical Gazette, Vol. 97, No. 539 (July 2013), pp. 224-233 (10 pages).
• Firdous Ahmad Mala, Some New Integer Sequences of Transitive Relations, J. Appl. Math. Comp. (2023) Vol. 7, No. 1, 108-111.

Crossrefs

Cf. A006905, A000110.

Formula

a(n) = A006905(n) - A000110(n+1).