The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A305858 a(n) = number of near-rings with n elements. 1
 1, 3, 5, 35, 10, 99, 24, 3858, 486, 535, 139, 54694, 454 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Near-rings are defined like rings but addition need not be commutative and multiplication need only left-distribute over addition (of course, right-distribution leads to an equivalent theory). Also, there need not exist a multiplicative identity. REFERENCES Gunter Pilz, Near-Rings: The Theory and its Applications, Revised Edition (1983), North-Holland Publishing Company. LINKS Table of n, a(n) for n=1..13. Choiwah Chow, Mikoláš Janota, and João Araújo, Cube-based Isomorph-free Finite Model Finding, Czech Tech. Univ. (Czechia, 2024). See p. 6. FORMULA Since all rings are near-rings, a(n) >= A027623(n). EXAMPLE The only near-ring of order 1 is the trivial ring, so a(1) = 1. There are 3 near-rings of order 2, all over Z2, so a(2) = 3. There are 5 near-rings of order 3, all over Z3, so a(3) = 5. There are 12 near-rings over Z4 and 23 near-rings over Z2^2, so a(4) = 12 + 23 = 35. There are 10 near-rings of order 5, all over Z5, so a(5) = 10. There are 60 near-rings over Z6 and 39 near-rings over S3, so a(6) = 60 + 39 = 99. There are 24 near-rings of order 7, all over Z7, so a(7) = 24. There are 135 near-rings over Z8, 1447 near-rings over D8, 281 near-rings over Q, 115 over Z4*Z2, and many over Z2^3, so a(8) > 1978. CROSSREFS Cf. A027623, A000001. Sequence in context: A221158 A068111 A162444 * A261659 A346715 A259853 Adjacent sequences: A305855 A305856 A305857 * A305859 A305860 A305861 KEYWORD nonn,hard,more AUTHOR Charles R Greathouse IV, Jun 10 2018 EXTENSIONS a(8)-a(13) from Choiwah Chow, Dec 18 2022 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 18 20:35 EDT 2024. Contains 376002 sequences. (Running on oeis4.)