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A078102
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1/6 of the number of ways of 3-coloring an (n-2) X n grid.
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1
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2, 27, 853, 63267, 11045757, 4547477370, 4419979346851, 10150938472416408, 55117503183129188479, 707887801249881516079368, 21511908182992495395699279579, 1547207013442473554135873920560606, 263429541331756165013316290711160389207
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OFFSET
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3,1
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COMMENTS
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Also the number of 3-colorings of the P_{n-2} X P_n grid graph up to permutation of the colors. - Andrew Howroyd, Jun 26 2017
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REFERENCES
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Michael S. Paterson (Warwick), personal communication.
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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 - 2, n]/2;
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CROSSREFS
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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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