A346008 Order of the full automorphism group of an n^2 X n^2 Sudoku puzzle.
1, 128, 3359232, 126806761930752, 17832200896512000000000000, 20122639448358307421277388800000000000000, 346671850578027965617950152200042758191185920000000000000000, 158635147791426908154211087484339310324630213259159597497553256448000000000000000000, 3135383389315524601627656266493367412334920325664589642523187933340624422000766361791574835200000000000000000000
Offset: 1
Keywords
Examples
For n=2, a(2) = 128 is the number of symmetries of a Shidoku puzzle. For n=3, a(3) = 3359232 is the number of symmetries of standard 9 X 9 Sudoku puzzle.
Crossrefs
Cf. A159299.
Programs
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Mathematica
Join[{1},Table[2*n!^(2*n+2),{n,2,9}]] (* Stefano Spezia, Jul 27 2021 *) -
SageMath
M = matrix(n^4,n^4) for i in [0..n^4-1]: for j in [0..n^4-1]: if i!=j: if i%n^2==j%n^2: M[i,j]=1 if floor(i/n^2)==floor(j/n^2): M[i,j]=1 D = Graph(M, format='adjacency_matrix') for col in [0..n-1]: for row in [0..n-1]: tl = n*col + n^3*row s = [] for i in [0..n-1]: for j in [0..n-1]: s.append(tl + i + n^2*j) D.add_clique(s) print(D.automorphism_group().order())
Formula
a(n) = 2*(n!)^(2n+2) for n > 1.
Comments