A078101 - OEIS

%I #14 Sep 16 2019 04:28:50

%S 1,9,187,9075,1034073,277458045,175605187731,262459366542859,

%T 927063711694234937,7743238400519517700687,

%U 152996488947929392223648350,7153582340115101979222478030231,791692010951982239786844983500390201,207426783553049237691620430245372971070275

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

%C Also the number of 3-colorings of the P_{n-1} X P_n grid graph up to permutation of the colors. - _Andrew Howroyd_, Jun 26 2017

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

%H Andrew Howroyd, <a href="/A078101/b078101.txt">Table of n, a(n) for n = 2..24</a>

%F See A078099 for formula.

%F a(n) = A207997(n-1, n) = A078099(n-1, n)/2. - _Andrew Howroyd_, Jun 26 2017

%t M[1] = {{1}};

%t 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 T[m_, 1] := 2^(m - 1);

%t T[1, n_] := 2^(n - 1);

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

%t a[n_] := T[n - 1, n]/2;

%t Table[Print[n]; a[n], {n, 2, 15}] (* _Jean-François Alcover_, Sep 16 2019 *)

%Y A diagonal of A078099 and A207997.

%K nonn

%O 2,2

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

%E a(7)-a(13) from _Alois P. Heinz_, Mar 25 2009

%E Name clarified and a(14)-a(15) from _Andrew Howroyd_, Jun 26 2017