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A078101 1/6 of the number of ways of 3-coloring an (n-1) X n grid. 2
1, 9, 187, 9075, 1034073, 277458045, 175605187731, 262459366542859, 927063711694234937, 7743238400519517700687, 152996488947929392223648350, 7153582340115101979222478030231, 791692010951982239786844983500390201, 207426783553049237691620430245372971070275 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

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

FORMULA

See A078099 for formula.

a(n) = A207997(n-1, n) = A078099(n-1, 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 - 1, n]/2;

Table[Print[n]; a[n], {n, 2, 15}] (* Jean-Fran├žois Alcover, Sep 16 2019 *)

CROSSREFS

A diagonal of A078099 and A207997.

Sequence in context: A274781 A293848 A266496 * A133556 A196215 A196682

Adjacent sequences:  A078098 A078099 A078100 * A078102 A078103 A078104

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 05 2002

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

STATUS

approved

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Last modified October 26 14:28 EDT 2021. Contains 348267 sequences. (Running on oeis4.)