A086265 Numerators of mean number of s-clusters in an n X n (0,1)-matrix.

1, 17, 897, 168529, 118183389

Offset: 1

Author

Eric W. Weisstein, Jul 14 2003

Keywords

• nonn
• frac
• more

Examples

			1/2, 17/16, 897/512, 168529/65536, 118183389/33554432...
		

Links

• Eric Weisstein's World of Mathematics, s-Cluster

Crossrefs

Cf. A002416.

Programs

Mathematica

For[n = 1, n <= 5, n++,
cnt = 0;
For[ii = 0, ii <= 2^(n^2), ii++,
  A = Partition[IntegerDigits[ii, 2, n^2], n];
  G = EmptyGraph[n^2];
  deleteG = 0;
  vert = {0, -1};
  horiz = {-1, 0};
  For[i = 1, i <= n, i++,
   For[j = 1, j <= n, j++,
    If[A[[i, j]] == 1,
     For[k = 1, k <= 2, k++,
      If[A[[i + vert[[k]], j + horiz[[k]]]] == 1,
       G = AddEdge[G, {j + (i - 1) n, j + horiz[[k]] + (i - 1) n + n vert[[k]]}];
       ]
      ],
     deleteG++;
     ]
    ]
   ];
  CC = ConnectedComponents[G];
  cnt += (Length[CC] - deleteG);
  ];
Print[cnt]
] (* Luca Petrone, May 09 2018 *)

Extensions

a(5) from Luca Petrone, May 09 2018