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A086265 Numerators of mean number of s-clusters in an n X n (0,1)-matrix. 1
1, 17, 897, 168529, 118183389 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..5.

Eric Weisstein's World of Mathematics, s-Cluster

EXAMPLE

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

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 *)

CROSSREFS

Cf. A002416.

Sequence in context: A221324 A124235 A218660 * A156138 A229261 A196873

Adjacent sequences:  A086262 A086263 A086264 * A086266 A086267 A086268

KEYWORD

nonn,frac,more

AUTHOR

Eric W. Weisstein, Jul 14 2003

EXTENSIONS

a(5) from Luca Petrone, May 09 2018

STATUS

approved

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Last modified March 25 10:19 EDT 2019. Contains 321470 sequences. (Running on oeis4.)