

A345317


Number of transitive but not symmetric relations on an nset.


0



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

0,3


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.


LINKS

Des MacHale and Peter MacHale, Relations on Sets, The Mathematical Gazette, Vol. 97, No. 539 (July 2013), pp. 224233 (10 pages).


FORMULA



EXAMPLE



CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



