A078102 - OEIS

%I #14 Aug 27 2019 09:51:55

%S 2,27,853,63267,11045757,4547477370,4419979346851,10150938472416408,

%T 55117503183129188479,707887801249881516079368,

%U 21511908182992495395699279579,1547207013442473554135873920560606,263429541331756165013316290711160389207

%N 1/6 of the number of ways of 3-coloring an (n-2) X n grid.

%C 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

%D Michael S. Paterson (Warwick), personal communication.

%F See A078099 for formula.

%F a(n) = A207997(n-2, n) = A078099(n-2, n)/2. - _Andrew Howroyd_, Jun 26 2017

%t 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;

%t W[m_] := M[m] + Transpose[M[m]];

%t T[m_, 1] := 2^(m - 1); T[1, n_] := 2^(n - 1); T[m_, n_] := MatrixPower[ W[m], n - 1] // Flatten // Total;

%t a[n_] := T[n - 2, n]/2;

%t Table[a[n], {n, 3, 15}] (* _Jean-François Alcover_, Aug 27 2019 *)

%Y A diagonal of A078099 and A207997.

%K nonn

%O 3,1

%A _N. J. A. Sloane_, Dec 05 2002

%E a(7)-a(14) from _Alois P. Heinz_, Mar 24 2009

%E Name clarified and a(15) from _Andrew Howroyd_, Jun 26 2017