A006609 Number of cyclic neofields of order n.

1, 2, 3, 8, 19, 64, 225, 928, 3441, 17536, 79259, 454016, 2424195, 15628288, 94471089, 679156224, 4613520889, 36563599360, 275148653115

Offset: 4

Author

N. J. A. Sloane, Simon Plouffe

Keywords

• hard
• nonn
• nice
• more

Comments

Also the number of (n-1,1)-partial orthomorphisms. - Pei Jisheng, Dec 06 2012; corrected by Max Alekseyev, May 17 2025

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• D. F. Hsu, Cyclic Neofields and Combinatorial Designs, Lect. Notes Math. 824 (1980). See p. 189.
• D. S. Stones, I. M. Wanless, A congruence connecting Latin rectangles and partial orthomorphisms, Ann. Comb. 16, No. 2, 349-365 (2012).

Formula

a(2n) = A003111(n-1). - Max Alekseyev, May 17 2025

Extensions

a(22) from A003111 added by Max Alekseyev, May 17 2025