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

%I A086265 #13 Feb 16 2025 08:32:50
%S A086265 1,17,897,168529,118183389
%N A086265 Numerators of mean number of s-clusters in an n X n (0,1)-matrix.
%H A086265 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/s-Cluster.html">s-Cluster</a>
%e A086265 1/2, 17/16, 897/512, 168529/65536, 118183389/33554432...
%t A086265 For[n = 1, n <= 5, n++,
%t A086265 cnt = 0;
%t A086265 For[ii = 0, ii <= 2^(n^2), ii++,
%t A086265   A = Partition[IntegerDigits[ii, 2, n^2], n];
%t A086265   G = EmptyGraph[n^2];
%t A086265   deleteG = 0;
%t A086265   vert = {0, -1};
%t A086265   horiz = {-1, 0};
%t A086265   For[i = 1, i <= n, i++,
%t A086265    For[j = 1, j <= n, j++,
%t A086265     If[A[[i, j]] == 1,
%t A086265      For[k = 1, k <= 2, k++,
%t A086265       If[A[[i + vert[[k]], j + horiz[[k]]]] == 1,
%t A086265        G = AddEdge[G, {j + (i - 1) n, j + horiz[[k]] + (i - 1) n + n vert[[k]]}];
%t A086265        ]
%t A086265       ],
%t A086265      deleteG++;
%t A086265      ]
%t A086265     ]
%t A086265    ];
%t A086265   CC = ConnectedComponents[G];
%t A086265   cnt += (Length[CC] - deleteG);
%t A086265   ];
%t A086265 Print[cnt]
%t A086265 ] (* _Luca Petrone_, May 09 2018 *)
%Y A086265 Cf. A002416.
%K A086265 nonn,frac,more
%O A086265 1,2
%A A086265 _Eric W. Weisstein_, Jul 14 2003
%E A086265 a(5) from _Luca Petrone_, May 09 2018