OFFSET
0,1
COMMENTS
a(n) is also the number of Arnoux-Rauzy factors of length (n+1) over a 3-letter alphabet. - Genevieve Paquin (genevieve.paquin(AT)univ-savoie.fr), Nov 07 2008
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
F. Mignosi and L. Q. Zamboni, On the number of Arnoux-Rauzy words, Acta arith., 101 (2002), no. 2, 121-129. [From Genevieve Paquin (genevieve.paquin(AT)univ-savoie.fr), Nov 07 2008]
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(0)=3, a(1)=9, a(2)=27, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Dec 29 2011
G.f.: -((3*(3*x^2+1))/(x-1)^3). - Harvey P. Dale, Dec 29 2011
MATHEMATICA
Table[ 3(2*n^2 + 1), {n, 0, 44}] (* Robert G. Wilson v, Aug 26 2004 *)
3(2Range[0, 50]^2+1) (* or *) LinearRecurrence[{3, -3, 1}, {3, 9, 27}, 50] (* Harvey P. Dale, Dec 29 2011 *)
PROG
(PARI) a(n)=3*(2*n^2+1) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
George E. Antoniou, Aug 25 2004
EXTENSIONS
More terms from Robert G. Wilson v and Mark Hudson (mrmarkhudson(AT)hotmail.com), Aug 26 2004
STATUS
approved