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A068253
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1/3 of the number of colorings of an n X n square array with 3 colors.
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4
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1, 6, 82, 2604, 193662, 33865632, 13956665236, 13574876544396, 31191658416342674, 169426507164530254380, 2176592549084872196370724, 66158464020552857153017287240, 4759146677426447759184119036493676, 810410082813497381147177065840601910384
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OFFSET
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1,2
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LINKS
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FORMULA
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MATHEMATICA
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M[1] = {{1}}; M[m_] := M[m] = {{M[m - 1], Transpose[M[m - 1]]}, {Array[0 &, {2^(m - 2), 2^(m - 2)}], M[m - 1]}} // ArrayFlatten; W[m_] := M[m] + Transpose[M[m]]; T[m_, 1] := 2^(m - 1); T[1, n_] := 2^(n - 1); T[m_, n_] := MatrixPower[W[m], n - 1] // Flatten // Total; a[n_] := T[n, n]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 12}] (* Jean-François Alcover, Nov 01 2017, after code from A078099 *)
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CROSSREFS
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See A047938 for number of improper colorings.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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