A078102 - OEIS

A078102

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

2, 27, 853, 63267, 11045757, 4547477370, 4419979346851, 10150938472416408, 55117503183129188479, 707887801249881516079368, 21511908182992495395699279579, 1547207013442473554135873920560606, 263429541331756165013316290711160389207

(list; graph; refs; listen; history; text; internal format)

OFFSET

3,1

COMMENTS

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

REFERENCES

Michael S. Paterson (Warwick), personal communication.

LINKS

Table of n, a(n) for n=3..15.

FORMULA

See A078099 for formula.

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

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 - 2, n]/2;

Table[a[n], {n, 3, 15}] (* Jean-François Alcover, Aug 27 2019 *)

CROSSREFS

A diagonal of A078099 and A207997.

Sequence in context: A300591 A251693 A182934 * A221534 A221535 A067075

Adjacent sequences: A078099 A078100 A078101 * A078103 A078104 A078105

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 05 2002

EXTENSIONS

a(7)-a(14) from Alois P. Heinz, Mar 24 2009

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

STATUS

approved