A078101 1/6 of the number of ways of 3-coloring an (n-1) X n grid.

1, 9, 187, 9075, 1034073, 277458045, 175605187731, 262459366542859, 927063711694234937, 7743238400519517700687, 152996488947929392223648350, 7153582340115101979222478030231, 791692010951982239786844983500390201, 207426783553049237691620430245372971070275

Offset: 2

Author

N. J. A. Sloane, Dec 05 2002

Keywords

• nonn

Comments

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

References

• Michael S. Paterson (Warwick), personal communication.

Links

• Andrew Howroyd, Table of n, a(n) for n = 2..24

Crossrefs

A diagonal of A078099 and A207997.

Programs

Mathematica

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 - 1, n]/2;
Table[Print[n]; a[n], {n, 2, 15}] (* Jean-François Alcover, Sep 16 2019 *)

Formula

See A078099 for formula.

a(n) = A207997(n-1, n) = A078099(n-1, n)/2. - Andrew Howroyd, Jun 26 2017

Extensions

a(7)-a(13) from Alois P. Heinz, Mar 25 2009

Name clarified and a(14)-a(15) from Andrew Howroyd, Jun 26 2017