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A078100 1/6 of the number of ways of 3-coloring a 4 X n grid. 4
4, 27, 187, 1302, 9075, 63267, 441090, 3075255, 21440547, 149482638, 1042187067, 7266087315, 50658875658, 353191693599, 2462438631411, 17168025532662, 119694800484387, 834507453158019, 5818153224352338, 40563936024707079, 282810170576026755 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also the number of 3-colorings of the P_4 X P_n grid graph up to permutation of the colors. - Andrew Howroyd, Jun 26 2017

REFERENCES

Michael S. Paterson (Warwick), personal communication.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (9,-15,6).

FORMULA

See A078099 for formula.

G.f.: x*(9*x-4-4*x^2) / (6*x^3-15*x^2+9*x-1). - Alois P. Heinz, Mar 23 2009

MAPLE

a:= n-> (Matrix([[27, 4, 2/3]]). Matrix([[9, 1, 0], [ -15, 0, 1], [6, 0, 0]])^n)[1, 3]: seq(a(n), n=1..30); # Alois P. Heinz, Mar 23 2009

MATHEMATICA

LinearRecurrence[{9, -15, 6}, {4, 27, 187}, 21] (* Jean-Fran├žois Alcover, Feb 13 2016 *)

PROG

(MAGMA) I:=[4, 27, 187]; [n le 3 select I[n] else 9*Self(n-1)-15*Self(n-2)+6*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Feb 13 2016

CROSSREFS

Row 4 of (1/2)*A078099.

Row 4 of A207997.

Sequence in context: A005974 A289718 A010910 * A036753 A164311 A091125

Adjacent sequences:  A078097 A078098 A078099 * A078101 A078102 A078103

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Dec 05 2002

EXTENSIONS

More terms from Alois P. Heinz, Mar 23 2009

Name clarified by Andrew Howroyd, Jun 26 2017

STATUS

approved

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Last modified October 22 22:35 EDT 2021. Contains 348180 sequences. (Running on oeis4.)