A006609 Number of cyclic neofields of order n. (Formerly M0882)

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

Offset

4,2

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

Table of n, a(n) for n=4..22.

D. F. Hsu, Cyclic Neofields and Combinatorial Designs, Lect. Notes Math. 824 (1980). See p. 189.

D. S. Stones and 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

Crossrefs

Sequence in context: A243335 A303835 A007999 * A005663 A112834 A042697

Adjacent sequences: A006606 A006607 A006608 * A006610 A006611 A006612

Keyword

hard,nonn,nice,more

Author

N. J. A. Sloane, Simon Plouffe

Extensions

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

Status

approved