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
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