Displaying 1-10 of 18 results found.
1, 1, 1, 1, 2, 2, 22, 563, 1676257
1, 2, 3, 5, 7, 29, 593, 1676860, 115620398393, 208904486974761399, 12216177524273716236243939
a(n) = 3*2^n.
(Formerly M2561)
+10
241
3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196608, 393216, 786432, 1572864, 3145728, 6291456, 12582912, 25165824, 50331648, 100663296, 201326592, 402653184, 805306368, 1610612736, 3221225472, 6442450944, 12884901888
Number of Latin squares of order n; or labeled quasigroups.
(Formerly M2051 N0812)
+10
39
1, 2, 12, 576, 161280, 812851200, 61479419904000, 108776032459082956800, 5524751496156892842531225600, 9982437658213039871725064756920320000, 776966836171770144107444346734230682311065600000
Number of reduced Latin squares of order n; also number of labeled loops (quasigroups with an identity element) with a fixed identity element.
(Formerly M3690 N1508)
+10
24
1, 1, 1, 4, 56, 9408, 16942080, 535281401856, 377597570964258816, 7580721483160132811489280, 5363937773277371298119673540771840
Number of species (or "main classes" or "paratopy classes") of Latin squares of order n.
(Formerly M0387)
+10
13
1, 1, 1, 2, 2, 12, 147, 283657, 19270853541, 34817397894749939, 2036029552582883134196099
Number of 1-factorizations of K_{n,n}.
+10
10
1, 1, 1, 2, 24, 1344, 1128960, 12198297600, 2697818265354240, 15224734061278915461120, 2750892211809148994633229926400, 19464657391668924966616671344752852992000
Number of n X n symmetric matrices whose first row is 1..n and whose rows and columns are all permutations of 1..n.
+10
10
1, 1, 1, 1, 4, 6, 456, 6240, 10936320, 1225566720, 130025295912960, 252282619805368320, 2209617218725251404267520, 98758655816833727741338583040
a(n) is the minimum absolute value of nonzero determinants of order n Latin squares.
+10
8
1, 3, 18, 80, 75, 126, 196, 144, 405
Maximum determinant of an n X n Latin square.
+10
8
1, 1, 3, 18, 160, 2325, 41895, 961772, 26978400, 929587995
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