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%I #12 May 11 2018 06:11:46
%S 1,17,897,168529,118183389
%N Numerators of mean number of s-clusters in an n X n (0,1)-matrix.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/s-Cluster.html">s-Cluster</a>
%e 1/2, 17/16, 897/512, 168529/65536, 118183389/33554432...
%t For[n = 1, n <= 5, n++,
%t cnt = 0;
%t For[ii = 0, ii <= 2^(n^2), ii++,
%t A = Partition[IntegerDigits[ii, 2, n^2], n];
%t G = EmptyGraph[n^2];
%t deleteG = 0;
%t vert = {0, -1};
%t horiz = {-1, 0};
%t For[i = 1, i <= n, i++,
%t For[j = 1, j <= n, j++,
%t If[A[[i, j]] == 1,
%t For[k = 1, k <= 2, k++,
%t If[A[[i + vert[[k]], j + horiz[[k]]]] == 1,
%t G = AddEdge[G, {j + (i - 1) n, j + horiz[[k]] + (i - 1) n + n vert[[k]]}];
%t ]
%t ],
%t deleteG++;
%t ]
%t ]
%t ];
%t CC = ConnectedComponents[G];
%t cnt += (Length[CC] - deleteG);
%t ];
%t Print[cnt]
%t ] (* _Luca Petrone_, May 09 2018 *)
%Y Cf. A002416.
%K nonn,frac,more
%O 1,2
%A _Eric W. Weisstein_, Jul 14 2003
%E a(5) from _Luca Petrone_, May 09 2018
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