cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A159191 Number of n-colorings of the Robertson graph.

Original entry on oeis.org

0, 0, 0, 24, 3490848, 3501104400, 564523119840, 31643453033640, 886834653776064, 15220684846368288, 181298924180884800, 1627952400490177080, 11672280987833510880, 69664869701930893104, 357038627052783076128, 1609181428647593728200, 6498071673405936462720
Offset: 0

Views

Author

Alois P. Heinz, Apr 05 2009

Keywords

Comments

The Robertson graph is the unique (4,5) cage: the quartic graph on 19 vertices (so 38 edges) with girth 5.

Crossrefs

Programs

  • Maple
    a:= n-> n^19 -38*n^18 +703*n^17 -8436*n^16 +73761*n^15 -500004*n^14 +2727105*n^13 -12246808*n^12 +45913333*n^11 -144701057*n^10 +383839223*n^9 -853388854*n^8 +1574465385*n^7 -2370057775*n^6 +2835163369*n^5 -2587310804*n^4 +1685281636*n^3 -693467820*n^2 +134217080*n:
    seq(a(n), n=0..20);

Formula

a(n) = n^19 -38*n^18 + ... (see Maple program).

A346008 Order of the full automorphism group of an n^2 X n^2 Sudoku puzzle.

Original entry on oeis.org

1, 128, 3359232, 126806761930752, 17832200896512000000000000, 20122639448358307421277388800000000000000, 346671850578027965617950152200042758191185920000000000000000, 158635147791426908154211087484339310324630213259159597497553256448000000000000000000, 3135383389315524601627656266493367412334920325664589642523187933340624422000766361791574835200000000000000000000
Offset: 1

Views

Author

Keywords

Comments

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

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

  • 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.
Showing 1-2 of 2 results.