login
A345317
Number of transitive but not symmetric relations on an n-set.
0
0, 0, 8, 156, 3942, 154100, 9414312, 878218390, 122207682476, 24890747805972, 7307450298831718, 3053521546328889460, 1797003559223742679800, 1476062693867018935173990, 1679239558149570227773844452, 2628225174143857306613215434524, 5626175867513779058706923151723150
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. 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.
FORMULA
a(n) = A006905(n) - A000110(n+1).
EXAMPLE
For n=3, a(3) = A006905(3) - A000110(4) = 171 - 15 = 156.
CROSSREFS
Sequence in context: A089669 A288682 A268543 * A113668 A120348 A251586
KEYWORD
nonn
AUTHOR
Firdous Ahmad Mala, Oct 02 2021
STATUS
approved