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%I #107 Apr 28 2023 19:59:50
%S 0,0,8,156,3942,154100,9414312,878218390,122207682476,24890747805972,
%T 7307450298831718,3053521546328889460,1797003559223742679800,
%U 1476062693867018935173990,1679239558149570227773844452,2628225174143857306613215434524,5626175867513779058706923151723150
%N Number of transitive but not symmetric relations on an n-set.
%C 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.
%C a(n) is even for all n.
%H Des MacHale and Peter MacHale, <a href="https://www.jstor.org/stable/24496798">Relations on Sets</a>, The Mathematical Gazette, Vol. 97, No. 539 (July 2013), pp. 224-233 (10 pages).
%H Firdous Ahmad Mala, <a href="https://doi.org/10.26855/jamc.2023.03.011">Some New Integer Sequences of Transitive Relations</a>, J. Appl. Math. Comp. (2023) Vol. 7, No. 1, 108-111.
%F a(n) = A006905(n) - A000110(n+1).
%e For n=3, a(3) = A006905(3) - A000110(4) = 171 - 15 = 156.
%Y Cf. A006905, A000110.
%K nonn
%O 0,3
%A _Firdous Ahmad Mala_, Oct 02 2021