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

1,2

Comments

a(n) is the order of the automorphism group of the n^2 X n^2 Sudoku graph (see A182866).

Links

Table of n, a(n) for n=1..9.

Formula

a(n) = 2*(n!)^(2n+2) for n > 1.

Example

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.

Mathematica

Join[{1}, Table[2*n!^(2*n+2), {n, 2, 9}]] (* Stefano Spezia, Jul 27 2021 *)

Prog

(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())

Crossrefs

Cf. A159299.

Sequence in context: A016879 A227661 A016939 * A017011 A196995 A214389

Adjacent sequences: A346005 A346006 A346007 * A346009 A346010 A346011

Keyword

nonn

Author

Carl-Fredrik Nyberg Brodda, Shay Jordan, Jul 27 2021

Status

approved