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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
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-François 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 * A356393 A036753 A164311
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 June 20 14:54 EDT 2024. Contains 373526 sequences. (Running on oeis4.)