A383036 The determinant of the matrix representing a totally anti-symmetric quasigroup of order 2*n+1.
0, 9, 1250, 352947, 172186884, 129687123005, 139788510734886, 204350482177734375, 389289535005334947848, 937146152681201173795569, 2782184294469515486371964010, 9986310782535957929474146174619, 42632564145606011152267456054687500, 213501642487388555901009081409220318757
Offset: 0
Examples
For n = 1, a(1) = 9 because: The resulting totally anti-symetric quasigroup has a matrix: with k = 1: 0, 1, 2, 2, 0, 1, 1, 2, 0 which has a determinant: 9. with k = 2: 0, 2, 1, 1, 0, 2, 2, 1, 0 has also the same determinant 9.
Links
- Paolo Xausa, Table of n, a(n) for n = 0..100
- H. Michael Damm, Totally anti-symmetric quasigroups for all orders n not equal to 2 or 6, Discrete Math., 307:6 (2007), 715-729.
- Wikipedia, Quasigroups
Programs
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Mathematica
A383036[n_] := n*(2*n+1)^(2*n); Array[A383036, 15, 0] (* Paolo Xausa, May 28 2025 *)
Formula
a(n) = n*(2*n+1)^(2*n) = A081131(2*n+1).
Comments