This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A345317 #107 Apr 28 2023 19:59:50 %S A345317 0,0,8,156,3942,154100,9414312,878218390,122207682476,24890747805972, %T A345317 7307450298831718,3053521546328889460,1797003559223742679800, %U A345317 1476062693867018935173990,1679239558149570227773844452,2628225174143857306613215434524,5626175867513779058706923151723150 %N A345317 Number of transitive but not symmetric relations on an n-set. %C A345317 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 A345317 a(n) is even for all n. %H A345317 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 A345317 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 A345317 a(n) = A006905(n) - A000110(n+1). %e A345317 For n=3, a(3) = A006905(3) - A000110(4) = 171 - 15 = 156. %Y A345317 Cf. A006905, A000110. %K A345317 nonn %O A345317 0,3 %A A345317 _Firdous Ahmad Mala_, Oct 02 2021