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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-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 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 June 20 14:54 EDT 2024. Contains 373526 sequences. (Running on oeis4.)